There has been suggestion elsewhere (cough) that the Balmer Lawn might not be good for parking. I 'm not sure about that, but I can suggest other venue if people are interested Alice Holt near Farnham in Surrey
Alice Holt Forest Woodland Park - DAYoutWITHtheKIDS.co.uk
It is similar to Balmer Lawn, there are things to do for kids (play area, climbing wall, large grassy area for games, nature trail with climbing frames in shapes of animals for active children etc), lots of long or short walks for health concious, bikes for hire. There is a nice picnic area next to pond and shaded by trees, although there are not many tables (around 4 I recon) but grassy area can be used for picnics. I thik the BBQ can bee booked, so will look into that if people are interested in the venue. Only charge is parking (lots of it and close so you can admire the line up

) and that is maximum £5 for over 4 hours stay, less than that if you want to stay shorter.
I don't know if there will be interest in the place but it is more centrally placed for London than New Forest, so I thought I might as well suggest it as I have already been there on numerous occasions and can thoroughly recommend it. What do you think?