There are a number of calculators on the web that will give you the diameter of a tire in the size you prefer. However, since every manufacturer seems to vary a bit from what is considered standard size, it is necessary to look at the manufacturer’s specification to get the dimensions they planned for their product and compare it to the very close to 26” Dunlop Road Speed size GregW has presented.
In general, common available models of modern radial tires seem to follow a pattern of the wider the tire the shorter the sidewall. In a 165 size, I have found that the 165R15 which used to translate to 165/85 R15 now sometimes is more like a 165/80 R15. Even when 2 manufacturers present a 165/85 R15 as their designation, I have found that there was as much as ½” difference in total diameter between then.
When my 64BJ8P1 was new, my original Dunlops lasted a little more then 6 months of city daily driving and weekends of 4 wheel drifting around PA mountain turns. My replacements, recommended by Healey and BMC, were Pirelli Cinturatos in 165R15 size. Although they held the road extremely well and matched the diameter, they were not as much fun.
As Steve and others have commented, you have a broad choice of tires that will fit but few that will come close to matching the actual diameter of the original Dunlop RS 590. The closest size matches, are for the most part, uncommon sizes and usually very expensive. I have chosen the Vredestein Classics in the 165 size and find them to be tall enough for my Phase 1 BJ8 (with the same frame and suspension as prior models and the added encumbrance of a transverse resonator) to clear all obstacles on a rough road… so far.
Good luck on your choice,
Ray (64BJ8P1)