I thought the Mk2 / S type rim was a 5j and then it went up to the E Type which had a 6.5J rim. My 5J wire wheel rims hold the 205/70/15.

 

I think 205 is as much as it's reasonable to 'stretch' to on a 5J rim. It will soften the ride and give some sidewall flex, but should be fine. Remember 205 is 8 inches. In the 1980s, it was common to adopt XJ6 disc wheels and tyres. I think the E type started with 5 inch rims and got to 6 on the series 3. Jaguar probably homologated wider sizes (and larger diameters) without offering them for sale.

 

Looks like I have some work to do!!