AIBU to think I can get accommodation & parking in London for £500?

This wasn't what the OP was asking about but it's also incorrect.

Up to 4 children under the age of 11 can travel with one fare paying adult on tube, buses, trains. You will need to pay for her if you use the clipper service or the cable cars.

Looking at some of the daily parking rates, I'm not sure why Heathrow is getting a bad response for parking.

You'll get cheaper, competitive hotels at Heathrow with plenty of hotels to choose from. Majority of hotels provide parking for £15-16 for 24 hours.

Buses every 5-10 minutes from Nene Road or Bath Road to go into the Heathrow bus terminal. 1.50 each. And regular tubes on the Picadilly Line.

Staybridge Suites on Bath Road are a decent price and if you get it on a deal, you'll get complimentary breakfast buffet

Look at Hanger Lane Premier Inn. We’re staying 4 nights in February, 2 adults and 10 yr old DD £290 and that’s with breakfast. Parking is £12 per night that you pay at the end of the stay. It’s right by Hanger Lane tube station (central line) or a short walk to Park Royal (Piccadilly line). We’ve stayed before, it’s about 25-30 mins on the tube to central London depending where you want to go.

Richmond travelodge is a good option. Richmond is lovely to walk around. Good walks by the Thames. Good tube access to South Ken for museums. Westfield close. I'd recommend Hampton Court which is an easy drive from Richmond.

You won't need the car when you are there so just train there and back.

Try the Premier Inn at Ealing and use the Elizabeth Line into London

Surely parking at Heathrow would be the most expensive parking option? You could park for free in lots of places in suburban London (on the street) but maybe pay for a driveway for convenience? I know areas such as Claygate, Carshalton, Chipstead where parking is easy and then trains are frequent. Then take a commuter train to a hotel in central London so you don’t have to spend your holiday commuting in and out of the suburbs?

Drive to somewhere in greater London where hotel prices are much cheaper, and take the tube in. I normally get a premier in in Wembley/harrow/Watford and take the tube inn. Works out so much cheaper

no need to drive into central london just find somewhere on outskirts-dont forget to factor in tube fares

We used to drive to premier inn Southgate - a few miles off the M25 and right by the tube station. Has relatively cheap parking.
now we usually go to the premier inn in Paddington basin - train then just a few minutes walk along the canal if you leave by the Grand Union Canal entrance. Can sometimes get rooms under 100 a night.

You would be better off getting the train into central London and finding somewhere there. Travelling in and out is tedious and even more so after a day of sightseeing.

Stay somewhere like Stratford which is next ti westfields in a premier inn or similar ! Easy to take the tube into town then for the other activities

take the train the whole way! I wouldn’t bother with a car at all- working costs even at Heathrow are insane

I think premiere inn in Chiswick has parking. And good rates.

Driving in central london is a fools game when there are so many other options

Get a family railcard and it’s even cheaper. I take DD regularly - we’re in South Wales and wouldn’t dream of driving.

This is a good idea OP. Ealing is easy too as long as the district line isn’t down.

we always drive to central London, there’s plenty of places to park. Westfield is a cheap parking option.

I'd suggest looking at somewhere on the Elizabeth Line. Ealing Broadway has relatively inexpensive parking and good links into town.

Slough is a good option just outside. There are several Premier Inns. In terms of someone saying it's 'grim' you'll literally just be travelling in, and the hotels are fine. You could tag on a Legoland trip if inclined 😀

£196 Premier Inn Plus, parking £10 per 24 hours (or £14 if no space in hotel) in Ealing and then Elizabeth line in.

We do this regularly - yes a bit of a journey on the train but it works for us.

Look at the YHAs. We stayed at one in Rotherithe last year. We had a 4 bed ensuite for 2 nights for a few hundred pounds. There are some more central ones too. We have also stayed at one in Goring, which was handy for the train to London.

Park at Westfield White City - its Shepards bush. It’s only £20 per 24hrs.

Then premier inn or motel one central somewhere . The Kensington one is probably ideal for museums.

If you’re not planning to use the car while you’re in London, why not just travel from Wales by train? Much faster and less stress. Use Booking.com to check accommodation options. Premier Inns are much nicer than Travelodge which are VERY basic, but both of those chains can be expensive compared to a B&B.

Your cheapest bet will be a family room and for 3 nights, that is definitely doable on £500. So search for that on Booking.com. Also look on Premier Inn website and find ones that are in the suburbs which will be cheaper, and just check whether there is a tube station nearby. If you’re near a tube station, getting around the attractions will be simple enough.