My car will have 185 70 15 tyres (corrected typo) fitted to the 6" wheels, what size are your tyres peter , I can see the car in a recent photo you have posted .
Thanks
Alan.
I have now fitted the 195/65 R15 Michelin CrossClimate tyres. They are a good option for me as by law in certain parts of Northern Italy we must have certified winter tyres or carry chains from 1st November to 30th April.
The 65 profile tyres have a sidewall of 195 x 65% = 126 mm (10mm more than the 60 profile tyres). Your 185/70 R15 tyres will have a sidewall of 185 x 70% = 129 mm so will give you good ground clearance

(for a Plus 4, that is)
A 6" rim is the maximum width for that tyre and will probably lower the overall height a fraction. The "Standard Rim Size" for the 185/70 R15 tyre is 5.00" x 15"
By the way the Vredestein Sprint Classic 185/70 R15 89 H are very well thought of in this tyre size and are not too expensive.