My XK -07 has 255/35 20inch tyres back on 9,5" wheels. This is not mentioned in the label in car's door, but I was told you can put a narrower tyre there with no problems. Car seller has spared some money :/ What do you think, are there any problems?

 

As long as the diameter difference front to rear isn't flagging the traction control they should suffice. The wheel lip should be inline with the tread or slightly narrower. Being wider is harder on the tire form but low riders have been doing it for years.

I'd be more concerned about curbing the wheel vs. rubbing the tire if you misjudge while backing along a curb. Maybe get some curb feelers since they worked for grandma.

 

Thanks. Perhaps previous owner was your granma, because wheels do have some marks on them...
Oh, I forgot Ranchero50: service was able to install one of your exhaust resonance removers, but the other pipe's bolts were so rusty they did not dare to open it. But the good news is that even that helped very much! So I am happy and grateful to you! Thank you man!

 

FWIW, traction control and ABS are looking for sudden changes in speed differential, not constant. Changing either front or rear height by a few percent won't affect either system, but the rear height will change speedo accuracy.