Brent.
You should see all sorts of grasses. Many of the courses you mentioned would have evolved out of what was in place in the first place and others would have just slowly received the native grasses from the area. There are obviously differences in species between the links and the inland courses and indeed more subtle differences between the heathland and downland tracks. On links it will mainly be fescue and bent on the fairways whereas inland courses will contain fescue and bent but also much ryegrass, meadow grasses (smooth stalked, rough stalked in the rough, and annual meadow grass) and things like crested dogs tail and Yorkshire fog, creeping soft grass, velvet bent, creeping bent. You name it.
If you are lucky enough to play Rye you will experience some greens with a very high fescue content (maybe 80%). These may not look much but they play as well as any of the new A and G strains of Pencross. Fescue though is really difficult to maintain on greens unless you’re willing to mow high and nearly all courses have suffered from the demands of the committee’s, just like everywhere else in the world and have shaved them down at some time in their lives and lost all the fescue. Generally though, on the inland courses you should see a bent and poa mix.
One thing’s for sure, you won’t see any Bermuda.
You will also see a mass of weeds or wild flowers as we are learning to call them. In fact golf courses in the UK can show incredible biodiversity, something that I believe is not so apparent on US courses.