Ville,
If nobody picks this up, ring The Addington (020) 8777 1055, I think they allow visitors on a Sunday. It's a short taxi ride from East Croydon Station (along Addiscombe Road to Shirley Road and Shirley Church Road where the golf club is located).
I also think that New Zealand will allow visitors if there is a space (01932-345049 or 01932 349619) (train to West Byfleet and short walk along Madeira Road and Sheerwater Road - passing West Byfleet Golf Club on the way).
Hankley Common also accept some weekend visitors, although it's a bit hard to get to - you'd need to take a train to Farnham and a taxi from there. (01252 792493 or 01252 793761)
West Surrey might also take you - it's about a 15 minute walk from Milford Station (01483 421275 or 01483 417278).
Mark.