As your aged MIL is not joining you, you could look at far larger or cheaper places in outer London. I doubt, with two pre-teens in tow, the last train back would be an issue. Try looking in leafy Surrey, but be sure it’s near a train station that will have you in central London in half an hour.
For example;
It’s half the price, near the Thames and a lovely big, historical park, and you’ll get to see a very different part of London, compared to the city centre.
Thanks for the advice everyone. After much browsing, we settled on a lovely 2 bedroom apartment in Southwark near London Bridge. I think it’s a good central here for us. I’m happy to spend a bit more and be closer to the centre of things and this came in at under £180/NT including fees.
My kids are 8 and 11 and are happy to share a bed, so no issues there.
I’m looking forward to showing my kids London!
I love London, and am happy for you that you can introduce your kids to it.
Enjoy!!!
And come back if you want any other London advice. Dopers don’t know everything, but wow are we opinionated!
I remember those ads, recalling old-fashioned phone snobbery.
I see the OP has already got a hotel. When I’m at the end of a trip around the UK, I usually stay at the Chiswick Palace hotel, between the Stamford Brook and Turnham Green Underground stops (although they’re both actually well above ground). It’s handy for getting to Heathrow in the morning, near to Kew if I want to spend my last day there, also not far from Kensington Palace if I want tea at the Orangery before I go home, and within walking distance of Chiswick House and gardens and Hogarth’s House.
Bumping my old thread for an update.
We left London yesterday after a glorious week there. We had one day with a short drizzle, but that was it.
The AirBNB was on Leathermarket St. in Southwark overlooking a park and had a wonderful view of London including the Shard. London Bridge Underground was about a 10 minute walk away.
Over the course of the week we walked about 90 km, used the tube extensively, rode one double decker bus, two Ubers, one black cab. We ended up seeing:
[ul]
[li]Greenwich, Cutty Sark, Royal Observatory[/li][li]Wicked and the Play That Goes Wrong[/li][li]Tate Modern[/li][li]Victoria and Albert[/li][li]British Museum[/li][li]Geffrey Musuem[/li][li]Borough Market[/li][/ul]
And a bunch of other stuff.
The girls had a great time!
Thanks to everyone for their suggestions and assistance.
Glad you had a great time. The weather in March can always be a bit iffy but I think in general it seemed like good “strolling” weather.
I’d be interested to hear of your highlights and do’s/dont’s
Leathermarket Gardens, in fact - I cycle by there sometimes on the way to work 
Pretty quiet spot, and a whole lot of stuff within 10 mins walk. Nice choice.
Glad it worked out!
I’m just travelling my tablet. I’ll type it up when I get back to a real keyboard!