Some perspectives of Syon Park cast me back to being in the Cotswolds what with the tractor, herds of cattle and fenced off fields. The Estate within the grounds of the park dates back to Tudor times and hosts various fun filled events in the year. Access to the park is free but expect to cough up £12.00 to enter the house, which is manned by gatemen during private events at weekends.
Not a particularly easy park to get to owing to the fact it's not remotely near an underground station. Your best bet is to take a train from Waterloo Station to Brentford via Barnes. Alternatively you can hop on the district line to Gunnersbury and walk 40 minutes to the edge of the park.