n.b. This is a Time Out-style list, having been assembled via a brainstorming exercise and thus with no basis in truth, objectivity or statistical research. If the list does genuinely contain the best things to do in London for £5, this is essentially a lucky accident.
1) A swim at the Hampstead Heath ponds(£4.50)
London's finest opportunity for cold swimming comes on the heights of Hampstead Heath where multiple open air ponds are available for a bracing splash. Pick from the Ladies' Pond, the Men's Pond and the Mixed Pond, at least two of which should be open to you from 7am daily. Payments can be made by cash or contactless card, but no change is given so if you turn up with a £5 note you won't get your surplus 50p back. Swimming at nearby Parliament Hill Lido costs the same, at least for the early and late sessions, but that won't give you the adrenaline hit a proper pond-dip promises.
2) Buy five tokens at Tim Hunkin's Novelty Automation(£5)
Tim's been making unusual automata for years, for example he's the man who designed the Secret Life of the Home gallery at the Science Museum. His Novelty Automation takes up the ground floor of a backstreet building near Holborn and admission is free. What you pay for are tokens to bring each of Tim's machines to life, and once each slot is filled you then stand back and watch to see what unfolds, or better still join in. I visited when it opened in 2015 and was very taken by the Instant Eclipse, intrigued by the Alien Probe and suspiciously hesitant of the Chiropodist. Delightfully bonkers. (blogged)
3) Descend into the Horniman Museum aquarium(£5)
Admission to the excellent Horniman Museum is free, which is great if all you want to see are the musical instruments and the stuffed walrus. But a small charge is made for the small aquarium, a basement attraction with 15 exhibits showcasing aquatic environments from around the globe, Watch clown fish dash, see a coral reef in action and contemplate the existential ennui of the poison tree frog. It's still the jellyfish I remember best of all, pulsing like neon against a large glass wall.
4) Watch a film at the Peckhamplex(£4.99)
Once upon a time Peckham had a Sainsbury's but in 1994 it was converted into a cinema and today it's an independent, commercial multiplex screening mainstream, independent, foreign language and art house films. Best of all watching a film still costs £4.99, the same as it has for over a decade, which probably puts your local cinema properly in the shade. Today you can pick between Guardians of the Galaxy 3, The Unlikely Pilgrimage of Harold Fry and of course Rye Lane, and that's just half of what's on offer. However 3D films cost £1 extra so don't try to use your fiver for one of those.
5) Climb Severndroog Castle(£4)
It's not really a castle, it's a commemorative tower built by a widow commemorating her husband's military exploits off the coast of Malabar. You'll find it at the top of Shooters Hill but you probably won't see it until you're very close because it's shrouded by trees. Some swear by the tearoom at the bottom but the big draw is a climb to the viewing platform on the roof (10 persons max) where the hills of Harrow, the masts of Croydon and Dartford Mental Hospital are clearly seen, depending on the weather. Even allowing for inflation, this fine folly should be doable for a fiver for many years yet. (blogged)
6) See the Aladdin Sane: 50 Years exhibition(£5)
David Bowie is in season on the South Bank on the anniversary of his iconic Aladdin Sane album, although it's the face-flashed album cover that provides the emphasis for this exhibionette. But you need to go before 28th May, and it's already quite booked up, and if you try booking online the grasping South Bank folk demand you create a profile and then add an optional £5 donation you have to delete, so for simplicity's sake probably best just turn up midweek and give them your money.
7) Buy a salmon and cream cheese beigel from Brick Lane(£4-ish)
King of all the foodstuffs sold in London, at least for the purposes of this list, is the salmon and cream cheese beigel from Beigel Bake on Brick Lane. Their salt beef classic is plainly a more iconic choice but that's over £6 so totally blows the budget. Normally I would throw in one of their fabulous carb-stuffed desserts as well, like the gooey Apple Strudel or a slab of Raisin Danish, except you won't quite have enough change for those either so basically it's a 70p jam doughnut or nothing.
The best London has to offer for a fiver (except you can't pay with a £5 note)
8) Ride a red hire bike for 90 minutes(£4.95)
London's bank-sponsored bike scheme has been running since Boris was Mayor, its clunky steeds available for hire in many an inner London location. Under the new charging scheme every 30 minutes you spend nipping between terminals costs £1.65, so for your fiver you can enjoy a 90 minute ride and still walk away with 5p change. That could get you from Regent's Park to the Olympic Park, or it could just allow for multiple circuits of Green Park if you're a bit shaky in the saddle. Cash is not accepted, however, so a £5 note gets you nowhere.
9) Ride a Thames Clipper(£3.80)
Thames Clipper fares alas crossed the £5 threshold in March, so Putney to Chelsea and Greenwich to Woolwich are now off limits. But one recent special deal undercuts a fiver, the Cross River fare, so if you fancy a short hop from Canary Wharf to Rotherhithe or Surrey Quays that's fine. Alternatively pull out all the stops and treat yourself to the full 9 minutes from Woolwich to Barking Riverside, a destination whose unbuilt delights are worth all of £3.80. Just remember to take a card because they too hate banknotes, and remember to sit out back and watch the estuarine splash because sitting in the cabin is for wimps.
The best London has to offer for a quid
10) Vist the Tower of London and Tower Bridge for £1 each(£2)
The best value deal in London, without question, is that residents of Tower Hamlets are allowed inside the Tower of London for £1. You have to bring your library card and proof of address, and you have to queue in person at the ticket office and hope all slots aren't sold out, but when full price is a massive £33.60 it is the best heritage bargain going. As for Tower Bridge, another world class icon, residents of Southwark, Tower Hamlets and the City of London get £1 entry there and that's another £11.30 saved. My apologies if you live in a lesser borough unable to take advantage of these offers, and my strongest encouragement to make use of this amazing deal if you possibly can.
The best London has to offer for a fiver (except it costs more than £5)
X) Buy a Groundling ticket at the Globe Theatre(£5 + booking fee)
How brilliant to watch one of the works of Shakespeare in a Thames-side theatre, standing throughout like a proper Tudor pleb. How brilliant too that the Globe release a fresh set of £5 tickets every Friday at 11am, a rock bottom price they've maintained for most of the 21st century. However these £5 tickets are only available online and every online order attracts a £2.50 transaction fee, so you can't slip into the Globe for less than £7.50. Hardly As You Like It, sorry, so shouldn't be on this list.
No longer the best London has to offer for a fiver(£5.25)
Until March it was possible to ride buses across London all day for less than a fiver, which was a phenomenal bargain. The daily cap is set at the cost of three single bus fares, which used to be £1.65×3 but is now £1.75×3, which alas breaks the bank by 25p. Every 'below a fiver' offer disappears eventually, and this sightseeing bonanza sadly just expired.