To be able to visit London on a budget in half term?

Yeah, get the National Express down, so much cheaper. Also look on booking.com for bargainous accommodation, 3 nights max is enough.

Family and friends rail card will work out cheaper than a disabled one.

When my children were young you used to be able to stay in rooms at Imperial College during holidays. Not sure if that was the half terms or just the long summer holiday.

A very unlikely one....is your husband in the forces as the Union Jack used to also have reasonably priced rooms.

Are there any youth hostels in London?

Try the premier inn hubs - stayed last sat and sun for 180 for two people will be cheaper for just one night. Rooms are small but the hotels are really nice! I

Commuter towns tend to come with expensive trains

Perhaps look at staying in zone 3?

And Christmas break

What is your AIBU?

Also check out the special events on at the Globe if she is interested in that - they always have things on in the school holidays and it's not expensive

For example she could take part in 90min workshop running during half term for £15 which would be something unique to have done and might be a help to GCSEs

https://www.shakespearesglobe.com/whats-on/romeo-and-juliet-workshop-12-16-years/

https://www.shakespearesglobe.com/whats-on/macbeth-on-stage-workshop-12-16-years/

The universities do let out rooms during the summer holiday only as the university half term isn't at the same time as the schools. University reading weeks are usually first or second weeks in November.

Do not stay at the premier inn excel we stayed there last week and it’s the only premier inn stayed in where I wouldn’t stay again. The car parking is free which was good but we were in the overflow and it was hard to get out as it’s not manned and there’s a barrier across so they have to phone through and then you have to wait half an hour for someone to come. There was also mice in the restaurant. I’ve booked for Stratford next Feb hopefully that might be better

I’d look East/Square Mile for cheaper hotels and get the tube in from there to central London. It’s only a couple of stops from that end. There’s also a viewing platform near Liverpool St station that is free but I can’t remember the name of it… You’ve also got Westfield in Stratford down that way for shopping.
Mayor of Scaredy Cat Town bar for mocktails? (Ask to see the mayor and they let you in the secret bit).
Agree with previous poster, Six the musical is brill and, at her age I reckon she’d love it!

https://www.yha.org.uk/stay

London has several YHA hostels where you can book a private en suite room for two people. Rooms tend to book out months in advance, I'd be surprised if you found anything now.

Your best bet is easy hotel in either Old Street or Victoria where rates start from £50.

EASY Hotel Old St slightly out of Central area so cheaper

The website says they have occasional places to rent a room

I'd also suggest Brick Lane and Spitalfields market - gives her a proper "London" experience that should be appealing to a teen and give her something that can't be done at home like eating in chain restaurants. Easily walkable from Liverpool Street Station.

There is a cool vintage market at Brick Lane to browse around
http://www.vintage-market.co.uk

And vintage shops like Rockit
https://www.rokit.co.uk/

Or a famous record store
https://www.roughtrade.com/en-gb/stores/east-london
Or a cool skateboard store: Slam City Skates

Brick Lane is famous for cheap curries but actually has a much greater range of food types (Japanese, Georgian, Mexican, Sichuan, crosstown doughnuts, a very fancy hot chocolate shop etc) including lots of tiktok popular options. Just put Brick Lane food in.

Fournier Street and Princelet street having amazing Hugenot era houses to wander past (Denis Severs museum is in one of them)

Spitalfields market is much fancier but has interesting street food and independent stalls selling clothes, art, jewellery as well as established brands in proper shops
There is a branch of affordable skincare line The Ordinary there with lovely staff who can help advise on a skin care routine at much lower cost than Sephora.

Look at cost of advance train tickets about 12 weeks before you travel when they get released. I got kids tickets between Edinburgh and London for £30 (return, with railcard) so I'm sure you can get that cheaper.

If she wants to go to Sephora how about looking for.accomodation in Stratford - it's very quick on the tube into central Londom and nice stuff there too, Olympic park, Hackney wick restaurants on canal.

You might be better on a Friend's and Family Railcard.
V&A museum currently has a TS exhibit
National Gallery is due to have a Van Gogh exhibit too

Premier Inn wise we normally stay at Stratford or Richmond as they are a little further out so cheaper - Richmond is an easy bus ride to Hampton court and a short walk to Kew.
DD is autistic though so we sometimes stay in the centre, Farringdon last time so that we can come back midday for a rest before going out for the evening, good access to Barbican tube and St Paul's and citylink.

Travel lodge is often a bit cheaper and the only real difference is no hairdryer. I often stay at the Vauxhall one for work and that has great public transport connections.

In October half term?

If you can travel down on the Sunday then hotels are cheaper on Sunday night. Like pp suggests, universities halls and yha are cheap

Look at the universities and see if there is non term time accommodation. The uni I work for does this and rooms are super cheap compared to hotels

It's perfectly feasible to stay further afield and travel into central London every day. I lived in many areas of London (zones 2-4) and it hardly took me longer than 20-30 minutes to get to central London.
Also worth looking into air-bnb and see if you can get a little studio or even a spare room in someone's house. I just saw a double room for £160 for 4 nights in Archway which is only about 15 min on tube from Tottenham Court road.

I'm not sure when half term is but I just searched Travelodge for end of October and you could get a night at the Greenwich one (which is in Deptford really- 2 mins from Deptford DLR - which is fun to go on!) for £45!
There are other locations for similar prices. Being near a station would be helpful. If you go too far out you'll end up spending a lot more on trains.

If you don’t mind driving, I’d look at one of the hotels around the Excel area that have free parking and then just get public transport in if your daughter can manage that. Might be cheaper than the train.

Try https://www.yha.org.uk/hostel/yha-london-lee-valley?utm_source=google&utm_medium=maps&utm_campaign=google-places

I don’t know what side you’re approaching from bit we have driven to the Premier Inn in High Wycombe before and got the train from there (£13, takes 30 to 35 mins).

I'd stay at Greenwich but a travelogue is still about £ 80 a night, from there you can visit the cutty sark, maritime museum, royal observatory, greenwich park, lace museum, Greenwich Market and get the user boat to the 02, then the other direction to the globe, Tate Modern and the Tate plus you pass a lot of landmarks. There are also many cheap places to eat, lots of noodle shops, Greg's and Weatherspoons.