A rider on a Dawes Galaxy can be seen on every Cycle Tourist Club ride.
Tyres for 27" are still available in the UK from places like
SPA although you cant get the latest high-techery. Switching to 700c wheels will give you a bit more tyre clearance to run wider tyres and the brakes can be adjusted for the slightly smaller diameter rim.
700c and 27" take the same inner tube.