Sorry to bump a dated topic, but this thread appears in the top page of Google search for "golfing with dogs in the UK" (these legacy threads become an informal Wikipedia on the web). The question is one we have been grappling with for a while and decided to create a list of all golf courses that welcome dogs. While the previous reply had a link to a list with 4 courses, this list has over 400 (plus reviews, tips, filtering to find one for you). So I thought that I would add it to the thread so people looking for dog golfing will find it easier to locate places to take their canine companions.
www.doggolf.info(PS. The site is purely non-commercial (no ads, sales, promo), just hopefully a useful reference for dog owners who play golf.