Staying near London with kids

[ScattyOnlySomeOfTheTime]

We want to book a Saturday night in London with 3dcs. They want to do London Eye. And the river cruise. See a few sites.
Hotels to fit all 5 are either expensive or unavailable by what I could see.

Dh suggested stay just outside London air b&b or a standard b&b. And train into London.

We are not well travelled. He would wing it for the travel But I have to have plans. Especially as youngest is 5.

So questions

Where is a good place to stay outside of London but not too far.
Has to be a simple journey into central London for the Eye.
Bonus if you've stayed before as a family of 5.

Where in the UK are you travelling from?

Havant Hampshire

I would look in Surrey. Guildford, Kingston, Surbiton, Esher, Woking etc are all on a direct line to Waterloo Station - Guildford, Surbiton and Woking especially have fast trains to Waterloo. Just don’t use them at rush hour!

There are two youth hostels in Dorking which I’m pretty sure have en-suite private rooms, which sleep five. From there it would be a short drive to Guildford and then direct train to Waterloo. Haven’t stayed there but we have family who are a group of 5 who use YHA private rooms a fair bit.