Welcome to the Club, Edmund.
First, let me say that you have a very nice car --- nice colour too.
At a guess, I think the issue could well be a fuel one. I have not driven a manual Jaguar for over 3 years, currently having a 2.7 Diesel S type - but as you car picks up better at a slower speed and is OK when it gets going I would suggest a fuel system cleaning additive --- under a tenner -- Diesel Magic, or Wynn's --- that will probably assist.
Regards,
Peter.