Sadly, there are also a fair number of NLEs: Newcastle/Royal Co Down; St Andrews/TOC; Caldy; Heswall; Woodhall Spa, R Worlington;.
Don't forget West Lancs on the Lancashire coast, Sheringham (if you include preserved steam. A few London Courses: Mitcham Junction and the former Prince's clubhouse (now Mitcham Common GC), Hadley Wood (quite a short walk from station to clubhouse), Totteridge and Whetstone (short walk to South Herts), Mill Hill East/Finchley GC, West Ruislip/Ruislip GC, Sudbury Town/Sudbury and Horsenden Hill GCs, South Greenford/Perivale Park, Perival/Ealing GC, Richmond/Royal Mid-Surrey, Barnes/Roehampton, Mottingham/Royal Blackheath, Fulwell/Fulwell, Strawberry Hill/Strawberry Hill, Wimbledon Park/Wimbledon Park, Sydenham Hill/Dulwich and Sydenham Hill (steep climb!), New Malden/Malden.
I seem to recall that West Byfleet and New Zealand are close to stations. West Surrey is close to Milford Station, West Hill is adjacent to Brookwood. I suppose (as of this morning) you can now get the train to Dawlish and walk to the golf course. Is there still a railway to Llandrindod Wells? Bramhall/Bramhall, Hillside/Hillside, Ainsdale/Southport and Ainsdale,