Playing the Royal St. George?
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Give the club a call and check so they don't have a competition on that day.
Ask if it's possible to play on that day. They might turn you down but if that happens
I would go there on the day and ask in person.
If that still doesn't work just drive to Prince's GC 1 mile away and play there instead.
It's almost as good!
Royal St George's is one of the remaining clubs on the Open rota that don't allow Lady members. I would imagine it takes its visitor restrictions pretty seriously, so unless you can find a member to play with you maybe out of luck.
However, you can but try and as Beach said Princes is supposed to be fantastic. Royal Cinque Ports is nearby too and like Princes is an ex-Open venue, it looks like it takes Saturday visitors but you will need to play in 2-balls.