I’ve been trying to get the Wife to agree to going also.
We usually park at Ikea, just off the North Circular & a few mins from the end of the M1. Has a huge multi storey that’s free & rarely gets full. Then out through Tesco, over the (ramped) footbridge to Neasden tube station. Done it plenty of times when our two were of buggy age. Need to check Ikea hours though. I even called & they said plenty of people park there & its fine as long as you pop in for a hot dog. 🙂
Other option we have done is parking at Seer Green just off the M40 & getting the train into Marylebone, but the train is quite pricey if you just turn up. (£10 return IIRC). Once your in London kids travel free (or they used to).