Hi, I have a Mk2 and the top was rebuilt by VSE (http://www.vse-engines.com/). Excellent job. I noticed on Youtube a specialist who may be worth a try in the absence of others replying : http://jaguarxkenginespecialist.co.uk/
There are others who advertise in the magazine also.
Hope you find someone, recommendation is key I think.
Mercedes A45 AMG
Mercedes AMG GLC43
Many years ago, I fitted a replacement 4.2 engine from VSE to my XJ6 Series III, and found it excellent. Also the gent with a van, a Mr Standen, who they used to deliver it (inevitably "Standen deliver"), who was surprisingly adept at wielding a breaker bar to remove various bits I should have from the old engine in part exchange.
They used to, and I expect still do, offer either an exchange engine, or (obviously with a wait) your own engine overhauled to the same standard.
1981 XJ6 Series III basket case
1991 XJS V12 "facelift"
2008 XJ TDVi