Will running 295/30 R20 instead of the stock 285/30 R20 rear tyres throw any fault code on a XKR 2008 with stock height?

 

No. I doubt it. What are the numbers after those sizes, ending in a letter?

 

105Y Speed and load rating.

 

I’m running 305/30/20 in rear with no problems.

 

on stock rims?

 

The old tires are 99Y and the new ones are 105Y. That's about 5% greater. Running 105s is acceptable, because Jag has some wheels at 103Z so you are in the neighborhood. As a result you will be faster on the radar, than on your car speedo.

 

NO, HRE 11.5 inch rears

 

No. I'm running 295's on my 2010 XKR and I've had no issues at all. Has stock suspension.

*Kumho PS291 tires

 

Likewise. 295s fit well. But it is really not like-for-like.
Do see https://tiresize.com/pressure-calculator/ for a reasoning and justification.

 

my initial concern was throwing off the traction control etc. So it seems 295/30 is still within the acceptable range.

 

Been running 295s since I bought my car, and I daily drive it. Of course I have aftermarket wheels on mine. 20×10's on the rear.

295s on rear, 255s up front.