Ten days in England and Scotland: the whole country out of one window

Nelson on a granite column, four Landseer lions at the base, and a fourth plinth in the north west corner that carries a new commissioned sculpture every couple of years. The National Gallery closes off the north side and is free if the weather turns.

London's fruit and vegetable market until 1974, now an iron and glass arcade with buskers licensed by audition working the piazza outside. The streets radiating off it are Theatreland, so this is where to look at what is on for the evening.

Five roads meeting under a wall of advertising screens and the winged archer everyone calls Eros, who is actually his brother Anteros and was cast in aluminium in 1893. Two minutes to look at, and the gateway to Soho behind it.

Ten minutes north puts you in the densest concentration of restaurants in Britain, from the Cantonese on Gerrard Street to small counter places off Berwick Street. Book for a weekend, walk in midweek.

Every coronation since 1066 has happened here, and a good proportion of the people who ran the country afterwards are underfoot: Poets' Corner in the south transept, Newton and Darwin in the nave, seventeen monarchs in between. Entry is charged, but evensong at five on weekdays is free and gets you the choir as well.

Barry and Pugin's neo-Gothic replacement for the palace that burned in 1834, built around the surviving Westminster Hall of 1097 with its astonishing hammerbeam roof. Tours run on Saturdays and through the recesses; the rest of the time it is a facade to walk past and photograph from the bridge.

Cross the bridge and turn left. Between County Hall and Blackfriars there are food stalls, a second-hand book market under Waterloo Bridge and enough wall to sit on.

A 135 metre wheel with 32 sealed capsules, turning slowly enough that a rotation takes half an hour and you never feel it move. On a clear day you see forty kilometres; on a grey one you see the inside of a cloud, so buy the ticket on the morning rather than weeks ahead.

Free, enormous and openly contested: the Rosetta Stone, the Parthenon sculptures and the Assyrian lion hunt, with the argument about how they got here written on the labels. Use the north entrance on Montague Place to skip the queue at the front.

The streets between the museum and Russell Square feed students and academics, which keeps the coffee good and the prices honest.

A vast Georgian quadrangle off the Strand, built for government offices and now an arts centre with fountains in the courtyard. The Courtauld Gallery upstairs is the reason to come: Manet's Bar at the Folies-Bergere, a room of Cezanne, and Van Gogh with the bandaged ear.

A round Romanesque church of 1185 built by the Knights Templar on the plan of the Holy Sepulchre, with stone effigies of knights lying on the floor. It sits in the Inns of Court, which are quiet lanes and gardens most Londoners never walk into.

Begun by William the Conqueror in 1066 and never finished being added to: a fortress, a mint, a menagerie, a prison and the strongroom for the Crown Jewels, which are on a moving walkway so nobody can stop in front of them. Go early, the jewels queue peaks after midday.

Borough Market is fifteen minutes west across the river and open most of the week. Leadenhall Market, a Victorian iron arcade five minutes north, is the alternative and empties completely at weekends.

The Victorian bascule bridge that half the world mistakes for London Bridge, still lifting several hundred times a year for tall ships. The high-level walkway between the towers has a glass floor and a small museum of the hydraulics; the road deck below is free.

The highest free viewing platform in London, on the 58th floor of an office tower in the middle of the City. Book a slot online, bring identification for the airport-style security, and go at dusk when the whole thing lights up beneath you.

Just under two hours on a fast service, several an hour. Book in advance for a fraction of the walk-up fare, and sit on the right for the flat country through Peterborough and Grantham.

The largest Gothic cathedral in northern Europe, built between 1220 and 1472 on top of the headquarters of a Roman legion, which you can go down and see in the undercroft. The Great East Window of 1405 is the biggest single expanse of medieval stained glass anywhere. The tower climb is 275 steps and worth every one.

A narrow medieval lane of butchers' shops with overhanging upper floors that nearly meet above your head, and the meat hooks still fixed to some of the frontages. It is the most photographed street in the north of England and unbearable at midday, so come at six when the shops shut.

Two miles of wall on a Roman and Norman rampart, the most complete circuit left in England, free and open until dusk. The stretch from Bootham Bar to Monk Bar looks straight down on the Minster and takes twenty minutes.

The smallest pub in York, an Edwardian room about the width of a corridor with a listed interior and Yorkshire ales on the pumps. Six people make it busy, which is part of the appeal.

Free, and the largest railway museum in the world: Mallard, which took the world steam speed record at 126 mph in 1938 and still holds it, a Japanese bullet train, Queen Victoria's saloon and a working turntable. Half a day disappears in here without effort.

Walk back in through Micklegate Bar. The market off Parliament Street has stalls doing everything from Yorkshire pies to Thai, and there are benches in St Sampson's Square.

Built directly over the Coppergate excavation of 1976, which found five metres of waterlogged Viking York with the timber and leather still intact. You ride through a reconstruction of the street, smells included, then look at what actually came out of the ground. Book a slot; the queue outside is long and pointless.

A quatrefoil stone keep of the 1240s on a Norman motte, with a new roof deck that gives you the whole city. It is also the site of the massacre of York's Jewish community in 1190, which the plaque at the bottom does not shy away from.

About two and a half hours. After Newcastle the line hugs the coast; Lindisfarne and Bamburgh Castle are both visible from the window if the weather allows.

The valley below the castle rock, drained in the eighteenth century and now a park with the railway running through the bottom of it. The floral clock at the east end has been planted every year since 1903.

A 61 metre Gothic spire over a seated statue of Walter Scott, blackened by two centuries of coal smoke and still not cleaned. The climb is 287 steps up a staircase that narrows as it goes and is not for anyone broad in the shoulders.

A small hill at the end of Princes Street covered in neoclassical monuments, including a Parthenon that ran out of money in 1829 after twelve columns and was never finished. It is the postcard view of the castle and the Old Town ridge, and it takes ten minutes to walk up.

A Victorian bar with an island counter, stained glass and Doulton tiled portraits of inventors around the walls. Order at the bar, stand at it, and look at the tiles.

A fortress on a volcanic plug that has been in use for eleven hundred years, holding the Honours of Scotland, the Stone of Destiny, and St Margaret's Chapel of about 1130, the oldest building in the city. The gun fires at one o'clock every day but Sunday, and everybody still jumps.

The high kirk of Edinburgh, with a crown steeple that has been the skyline of the Old Town since the 1490s. John Knox preached here through the Reformation; the Thistle Chapel of 1911 in the corner is absurdly ornate and easy to miss.

The Mile itself sells tartan and shortbread. Duck down Cockburn Street or into the Grassmarket, both two minutes away, and the food improves immediately.

The King's residence in Scotland, at the bottom of the Mile, with the ruined abbey of 1128 attached to the back of it. The chambers upstairs are where Mary Queen of Scots watched her secretary Rizzio dragged out and stabbed in 1566. Closed for roughly a week each summer when the King is there, so check before you walk down.

The high point of Holyrood Park, a volcanic remnant with the whole city, the Firth of Forth and Fife laid out below it. Several paths up; the one from the Holyrood car park past the loch is the gentlest and the Salisbury Crags route is the dramatic one.

Come off the hill at Holyrood and walk back up the Canongate. The cafes around St Mary's Street do breakfast until noon and you will have earned it.

Free, and the best museum in Scotland: a Victorian iron and glass gallery full of light attached to a modern block covering everything from the Lewis chessmen to Dolly the sheep. The roof terrace is public and hardly anybody finds it.

Also free, on the Mound between the Old Town and the New: Titian, Vermeer, Raeburn's skating minister and a strong Scottish collection in the basement. An hour is enough and it is on the way back to Princes Street.

A tall narrow house of 1622 up Lady Stair's Close, given over to Burns, Scott and Stevenson: manuscripts, a printing press and Burns's writing desk. Free, forty minutes, and the close outside has quotations set into the paving.

The tram from St Andrew Square takes about half an hour to the terminal and runs every seven minutes. The airport bus is cheaper and about the same speed.