Eight days in London, Bruges and Amsterdam: three countries and not one airport

Nelson on his column, four bronze lions added by Landseer in 1867, and a fourth plinth that has held a different commissioned sculpture every couple of years since the scheme began in the late 1990s. Protests, football celebrations and pigeons, all in the same fortnight.

The church on the corner of the square, with a portico that got copied across colonial America. The crypt underneath is a cafe with brass rubbing in the corner, and the church has run a shelter for rough sleepers since the First World War.

The old fruit and vegetable market of London, now a covered arcade of shops with street performers working the piazza outside on a rota. Touristy and knows it, but the ironwork is Victorian and the surrounding streets are where the theatres start.

Fifteen minutes north on foot puts you in the densest eating in Britain, from Cantonese on Gerrard Street to small Italian rooms off Charlotte Street. Book if it is a weekend, walk in if it is not.

A coronation church, a royal burial ground and a national attic all at once, with Poets' Corner in the south transept and the Cosmati pavement in front of the high altar. Entry is charged, but a service is free: choral evensong at five on weekdays gets you the building and the choir for nothing.

The neo-Gothic pile Charles Barry and Augustus Pugin built after fire destroyed the old palace in 1834, wrapped around the surviving medieval Westminster Hall. Tours run on Saturdays and when Parliament is in recess; otherwise the walk past it and over the bridge is the view everyone photographs.

The stretch between the London Eye and Blackfriars has food stalls, a second-hand book market under Waterloo Bridge and enough benches to eat outside when it is dry.

An open-roofed oak and lime-plaster reconstruction of Shakespeare's theatre, finished in 1997 a couple of hundred metres from where the original burned down. The summer season plays without stage lighting or amplification, and the standing tickets in the yard are the cheapest way into any theatre in London.

Free, vast, and openly argued about: the Rosetta Stone, the Parthenon sculptures and the Assyrian lion hunt all sit here with the question of how they arrived on the labels. Go in at the Montague Place door on the north side and skip the queue at the main gate.

The streets between the museum and Russell Square are full of small cafes serving the university, which means decent coffee at student prices rather than museum-forecourt prices.

A fortress begun by William the Conqueror in 1066 and added to by everyone since, holding the Crown Jewels, an armoury and nine hundred years of imprisonment and execution. The Yeoman Warder tours are included and are the best hour in the place, so catch one at the gate.

The Victorian bascule bridge everyone mistakes for London Bridge, still raised several hundred times a year for river traffic. The high walkway has a glass floor and a view back at the Tower; the free version is simply to walk across the road deck at dusk.

Under two hours to Brussels-Midi, then about an hour more on a Belgian domestic train. Buy the second leg at the machine on arrival rather than in advance; there is no reservation and no saving.

A hectare of square with the belfry on its south side, 83 metres and 366 steps up to a carillon of 47 bells that still gets played by hand. Climb it early or not at all: the staircase is single file and they cap the numbers at the top.

Two churches stacked on each other on the Burg: a plain Romanesque chapel of the twelfth century underneath, a rebuilt Gothic one above holding a rock crystal vial said to contain the blood of Christ. It is brought out for veneration at set hours, and paraded through the town every Ascension Day.

A bar down an alley barely wide enough for two people, pouring an eleven percent house tripel that they will only serve you three of. Cheese with it, no music, and a rule about no more than that for good reason.

The restaurants ringing the main square charge for the view and cook accordingly. Walk five minutes north into the lanes around Sint-Jakobsstraat and the same money buys a much better plate.

A brick tower of 115 metres, the second tallest brickwork tower anywhere, over a church holding Michelangelo's Madonna and Child. Bought by a Bruges cloth merchant in 1504, it is the only sculpture of his that left Italy in his lifetime. The tombs of Charles the Bold and Mary of Burgundy are in the choir behind it.

A medieval hospital that treated the sick for seven centuries, with the wards intact and six paintings by Hans Memling still in the building they were made for. The Shrine of St Ursula, a gilded reliquary painted like a tiny cathedral, is the one to stand in front of longest.

Six centuries of painting in a small museum, but everybody is here for two rooms of Flemish Primitives: van Eyck's Madonna with Canon van der Paele of 1436, painted with a precision nobody had managed before, and Gerard David's uncomfortable Judgement of Cambyses.

The water east of the Burg, around the Groenerei and the Rozenhoedkaai, has benches and a couple of small kitchens. Fries from a friture and a bench beats a terrace with a view tax.

The last brewery still making beer inside the walls, and since 2016 it pumps the finished product to its bottling plant through three kilometres of pipe under the streets rather than by lorry. The tour ends on a roof terrace with a glass of Brugse Zot in your hand.

Around three hours thirty in total, changing at Antwerp-Central. Leave a little time in Antwerp if the connection allows: the station opened in 1905 and now runs trains on three stacked levels under a domed hall.

Built between 1620 and 1631, and at 85 metres still the tallest church tower in Amsterdam. Rembrandt is buried somewhere inside in an unmarked pauper's grave, the exact spot lost. The tower is climbed by guided tour only and the slots are small.

The canal house where the Frank family hid for two years behind a hinged bookcase, kept deliberately bare: no furniture, the original diary in a case, and the rooms left as they were found. It takes about an hour and it is quiet on the way out.

The grid of small streets north and west of the Westerkerk is where Amsterdam eats without queueing. Brown cafes serve proper food until late and take walk-ins on weeknights.

Eight hundred years of Dutch art in a building that is itself worth the ticket. The Gallery of Honour runs Vermeer, Hals and Steen up to The Night Watch of 1642 at the far end, a militia portrait so large it was cut down in the eighteenth century to fit a doorway.

The lawn between the two museums has kiosks and, in summer, deckchairs. For something better, cut two streets east into the Pijp where the prices halve.

About two hundred paintings and five hundred drawings, hung chronologically so you watch the palette go from Dutch brown to Provencal yellow across two floors. Tickets are online only with a time slot, and the last hour of the day is the calmest.

The city's main park, five minutes west of the museums, full of joggers, picnics and an open air theatre in summer. Enter at the Stadhouderskade end and walk the length of it to come out near the Overtoom.

A walled courtyard of houses a few steps off the shopping street, founded for lay religious women and still lived in. Number 34, Het Houten Huys, dates from about 1420 and is one of only two wooden houses left standing in the centre of Amsterdam. Enter quietly; people are at home.

Fifteen to twenty minutes from Centraal, several an hour, and the platforms are directly under the terminal. Tap in with the same contactless card you have been using all week.