Things to do this week for £5 or less.

1. Investigate the unexplained with London Fortean Society

We don't know how they do it, but London Fortean Society never fail to come up with a fascinating topic for their monthly meeting, open to anyone. This time they're welcoming Eric Huang, host of Saint Podcast, for a talk about the phenomenon of stigmatics — people who appear to bear the wounds of Jesus's crucifixion on their own body.

Hear about the history of mysterious (and painful) stigmatics, and how it remains a controversial marvel today, over a pint or two at The Miller near London Bridge.

A History of Stigmata at London Fortean Society. Tickets £5, 4 October

2. Take a trip from Singapore to London

If you've got itchy feet, but your budget doesn't stretch to international travel right now, Stanfords travel bookshop in Covent Garden is always a good bet. This week, hear from Alex Bescoby, author of new book The Last Overland, about the 13,000 mile road trip he took through 23 countries to bring a Land Rover home from Singapore to London.

To be precise, it's the same Land Rover driven by a team in the opposite direction back in the 1950s, resulting in a documentary in which David Attenborough was involved. Hear Bescoby's thoughts on his own 2019 journey, and how the world has changed in the time between the two journeys, ahead of a new documentary airing in the autumn.

The Last Overland by Alex Bescoby at Stanfords, Covent Garden. Tickets £5, 5 October.

3. Witness the hidden stories of Bangladeshi seamstresses

A long-term local history project comes to fruition with opening of free exhibition Home Seamstresses: I Sewed, I Sewed, I Sewed.

It tells the stories of first-generation Bangladeshi women living in the East End between 1975-1995, many of whom are now in their 60s and 70s. They worked from home as seamstresses to support their families, an industry which has boomed and declined in their lifetimes, and told their stories to heritage oral historians and researchers, who compiled their memories into a book and this exhibition.

Home Seamstresses at Rich Mix, Shoreditch. FREE, 5-24 October.

4. Celebrate NASA's African-American women with a screening of Hidden Figures

If you're anything like us, you intended to see Hidden Figures when it came out in cinemas, but never quite got round to it.

Fret not, there's a chance to watch it this month, as part of London's Black History Month programme of events. The 2016 film tells the true story of three female African-American mathematicians working at NASA during the early years of the US Space Program. Katherine Johnson, Mary Jackson and Dorothy Vaughan worked in a unit which was still segregated by race, yet their work was crucial in the launch and safe return of astronaut John Glenn, the first American to orbit the Earth.

Hidden Figures at Fairfield Halls, Croydon. Tickets £3, 6 October.

5. Ogle vintage vehicles at the Classic Car Boot Sale

One of the most photographed events in London returns to King's Cross. The Classic Car Boot Sale sees dozens of vintage vehicles — from mopeds to trucks — parking up in Granary Square. And there's good news for bargain hunters, as vintage clothing, homewares, records and more are sold — just like a regular car boot.

Sustainability is a key factor, and new for this edition is the Suitcase Sale, a selection of smaller, curated area of clothing, as well as a Repair Shop, with workshops to help you make your clothes and vintage items last longer, and a Charity Supermarket, where you can rummage through goods from 11 different charity shops.

As always, DJs spin tunes from the top deck of a Routemaster, and dressing up (and dogs!) are encouraged, though not essential.

Classic Car Boot Sale, King's Cross. Tickets £5, 8-9 October.

6. Celebrate Diwali in Trafalgar Square

Diwali falls on 24 October this year, but London's celebrations get under way early with the huge Diwali on Trafalgar Square. Join people from several different countries and religions, including Sikhs, Hindus, Buddhists and Jains, to celebrate the triumph of good over evil in the Festival of Light, with traditional music and dance performances, Indian street food, and plenty of information about Diwali for anyone who isn't familiar with the festival.

Diwali on Trafalgar Square. FREE, 9 October

7. Learn something new about Enfield's history

Ever heard of the lost Tudor palace of Elysing? It was a building in Enfield, and its exact location remained unknown until excavation works in the 1960s. That's just one of 13 stories about Enfield told in a travelling exhibition, which can be seen at Forty Hall this week. You can also learn about Bangladeshi migration, a famous poet, and plenty more.

Stories of Enfield Travelling Exhibition at Forty Hall. FREE, until 11 October.

8. Pay what you want to see Lucien Freud's artworks

One of the biggest exhibitions in London this autumn is National Gallery's Lucian Freud: New Perspectives — but with tickets upwards of £20, it's not in everyone's budget. Unless you go on a Friday night that is, when tickets are 'pay what you wish' (minimum £1). That's anytime after 5.30pm, any Friday during the exhibition, but these tickets are bound to be popular, so you'll want to book in advance.

Pay what you wish Lucian Freud at National Gallery. 7 October and every Friday until January 2023.

9. Have a smashing time at London's conker championships

There's not one, but two chances to get involved in stampsies and nut-pimping (nope, we don't know either) this weekend, with a duo of conker championships taking place.

Head south on Saturday for the Peckham Conker Championships, held in a brewery (what could possibly go wrong...?), with both adults (16+) and kids competition categories. The prize? "The Golden Nut" — a 22 carat gold conker.

Then on Sunday, the Hampstead Heath Conker Championships bring Londoners together for an afternoon of autumnal nature activities, live music, and the all-important contest.

Peckham Conker Championships at Brick Brewery Tap Room. FREE, 8 October.

Hampstead Heath Conker Championships at Parliament Hill Bandstand. FREE, 9 October

10. Track down powerful stories about the Transatlantic slave trade

Noticed arty globes popping up around central London recently? That'd be The World Reimagined, four different sculpture trails featuring painted globes, each one telling a story from "the history, legacy and future of the Transatlantic Trade in Enslaved Africans".

Find them in locations such as Covent Garden, Fenchurch Street and St Paul's, each one designed by a different artist. They're in situ for the rest of the month, so plenty of time to wander around tracking them all down.

The World Reimagined. Free, until 31 October.

Looking for more free things to do in London? Here are 102 of em!