I've seen and heard of others installing Eibach lowering springs on their XF/XFR's, however, per their website's application search they don't even offer springs for our cars. For those who have "successfully" installed Eibach springs with NO issues, which specific spring Part # would fit the XFR?.
I'm currently waiting on custom wheels with a 5 week waiting period for fabrication. I'm thinking I'll be lowering the car to cancel out the wheel gap that's currently present.

 

Part # 4513.130.
Made to fit the 2008-2010 4.2 V8, see here: Eibach Jaguar Lowering Springs | 2008-2010 Jaguar XF (4.2L V8) Eibach Pro-Kit Performance Springs
I fitted a set of these exact same springs to my 2010 XFS (3.0 litre V6 twin turbo diesel) and they fitted and worked perfectly. 1" drop at the rear, 1.2" drop at the front, improved the stance, look and cornering no end, with very little loss of ride comfort.
I haven't (yet) pulled the trigger on a set for my R as I'm not entirely sure they will fit properly and not cause problems with the active suspension on the R.

 

Definitely appreciate the information, I'll wait and see how the new wheels look upon installing them. I didn't stray from the 20in diameter wheels so I can't imagine less of a wheel gap. I pondered the 21in wheel but at the end I went with 20x8.5 and 20x10 (Avant Garde M510 in Gloss black)

 

I'll post pics of installed wheels in about 4 weeks....can't wait.

 

Whether the gap narrows or not depends on the tyre profile you choose. Generally you would need to put a lower profile tyre on a larger wheel to keep the speedo accurate and not gear the car up.

For instance when replacing an 18" wheel with a 55 tyre profile with a 20" you would need to go to a 30 profile tyre to get the rolling diameter similar.
So in this case your gap would remain almost the same.

If you went to a 35 profile your gap would reduce by 6cm but your speedo would be a little out.

Have a play with this calculator.

Visual Tyre Size Calculator | Kouki Tech

 

Completely understand...
I'm going with 255/35/20 Front and 295/30/20 Rears