The problem with this is the traffic heading into Putney and back after the game. Any roadworks (like there were last season) will see the main drag very slow in moving. Personally I would drive to Surbiton and park at the station (a fiver on a Bank Holiday) then train/tube to Putney Bridge...
Just looked on 'parkonmydrive' and there's a space on Upper Richmond Rd (2 minutes from Putney Station) for £2 (for a part of day booking/£15 all day) But there are others on the southern end of the District Line tube towards Wimbledon then 3/4 stops to Putney Bridge