To fully round off this thread from my point of view - I have now had a set of 5 195/65/R15 Dunlop Bluresponse tyres fitted at a local tyre specialist - Harry Park aka Kendal Tyres. I took the Smoothride cones and the spare in to them, to check they would fit their balancing machine, before actually ordering the tyres.
It all sent very smoothly, with suitable care for the rims and sealing bands. They used adhesive weights on the inside of the rims and were happy to put just the usual 22psi in them. I've not driven the car yet, as I'm doing a couple of other jobs while it is up on axle stands, but I anticipate a better ride and better grip with some new rubber - the other tyres were the originals, manufactured in 2016 so getting on a bit.