| Things to do this week for £5 or less. The Lord Mayor's Show is on Saturday. Photo: City of LondonRemember to watch out for train and tube strikes this week. They're happening on Monday 7, Wednesday 9 and Thursday 10 November. Full details of what's affected here, but be aware that there's likely to be a knock-on effect the morning after strike days — which basically means disruption for most of this week. 1. Behold a Dichroic Sphere Head down to the Riverside Terrace at Southbank Centre on Monday to see Jakob Kvist: Dichroic Sphere. The work by the Danish light artist uses acrylic sheets and dichroic film on an aluminium structure to cast multicoloured light in different directions, using just a single, energy-efficient bulb. (Obviously it's best viewed in the dark.) We expect it to be all over Instagram this winter. Free, 7 November-8 January. 2. Watch a Nordic noir play in Hackney Three actors, 28 characters, one true story. That's the setup for The Wetsuitman, a play about a retired architect who finds a washed-up wetsuit, and the remains of a body inside it. It's on at the Rose Lipman Building in Haggerston, with tickets being sold on a pay what you can basis. Pay what you can, 8-13 November. 3. Be enchanted by London lighting up for Christmas Carnaby is one of the areas switching on its Christmas lights this weekWith the Oxford Street Christmas lights already aglow, other areas of London follow suit this week. Carnaby and Covent Garden are lit up from Tuesday, with Regent Street and St James joining in on Wednesday, followed by Marylebone on Thursday. See our full guide to when London's Christmas lights are switched on, and check with individual locations for details of special switch-on events and parties. Free, 8-10 November. 4. Garland for the Queen The late Queen had many links with the Southbank Centre — attending the opening of the Royal Festival Hall as part of the Festival of Britain in 1951, and making several return visits throughout her reign. Following her death, Southbank Centre opened a display, A Garland for The Queen. This week is your last chance to catch the exhibition, as it closes on Tuesday. On the final day, there's also a free event, with archive staff showing material never seen in public before. Free, until 9 November. 5. Go on a Monopoly world tour Monopoly Travel World Tours pops up at Noho Studios in Fitzrovia for two days (Friday and Saturday), inviting young adventurers and their families to go on a 'world tour', exploring the Great Barrier Reef, helping to build the Great Wall of China and enjoying the festivities at Colombia's Carnaval de Barranquilla. The free, 30-minute session ends with the opportunity to enter a competition to win an actual trip somewhere exotic. Book your slot in advance. Free, 11-12 November. 6. Watch the spectacle of the Lord Mayor's Show Pomp, pageantry and an almost comically extensive parade come to the City of London on Saturday for the Lord Mayor's Show, which is free to watch from anywhere along the route. The annual tradition dates back more than 800 years, with the new Lord Mayor riding in the golden State Coach from Mansion House to the Royal Courts of Justice, flanked by a procession that's three miles long! Our guide to the Lord Mayor's Show has an overview of the day, and tips on the least busy places to watch. Plus, the 'Ghost Parade' is likely to take place around the City in the early hours of one morning in the run-up to the Show — but as it's a non-publicised event, we don't know when it'll be. Free, 12 November. 7. Get free entry to St Paul's Cathedral Free entry? Yes please! Photo: Matt BrownAs part of the Lord Mayor's Show celebrations, St Paul's Cathedral opens to the public for free, 8.30am-last entry 3.30pm, for one day only. Free entry applies to the Cathedral floor only, but that'd normally set you back £18 for an adult ticket, so this is quite the steal. If you do want to go up to the dome, that's £10 extra. Alas, you can't book free tickets, so it's a case of getting there early and hoping you get in — just remember there are road closures in place and the City will be very busy on the day. Free, 12 November. 8. Take a last wander around Frieze Sculpture Park This is the final week of Frieze Sculpture 2022, the free, open-air art trail which pops up alongside the much more spenny Frieze Art Fair. Wander around Regent's Park, hunting out 19 large-scale sculptures by artists from around the world. You can learn more about this year's works with this free guide — and you're probably just in time to see the autumn leaves in Regent's Park, too. Free, until 13 November. 9. Go for an autumnal stroll in Epping Forest Perfect time to head Epping way. Image: Peter Trimming in WikicommonsSpeaking of autumn leaves, right now is a gorgeous time to get out to get out to Epping Forest, and bask in the golden/orange brilliance of the foliage. The forest (or parts of it at least) is easily accessible by public transport, and you'll find various visitor centres, pubs and cafes dotted around the area, so you can make a day of it. Looking for more free things to do in London? Here are 102 of em! We've also compiled this epic map of free stuff in London. | 