Suggest you phone Kew and ask.
There is limited parking on the road by the Lion and Victoria
gates but that is also likely to be full if you think the car park might be full by the time you arrive.
Kew on Sunday at this time of year is likely to be absolutely rammed. A friend of mine gave up and left recently because the queues to get in were so long.
Do you absolutely have to drive there? You can get the district line from Victoria to very near the main gate (the car park is near a gate quite a way away from the main part of the gardens, I think).
Alternatively, we recently got a train from Vauxhall to Richmond and then a bus to the main gate. We had two kids with us and they didn't moan too much about the length of the journey
ETA: Vauxhall to Richmond is only a few stops.
Edited 2 time(s). Last edit was june 08, 08:36am by Sue.