Martin
I feel your mechanic is going to struggle to see if the CAT is, as you put it "blocked", without removing it, which is not a simple five minute job. He may however be able to hear, by tapping it heavily with his fist, if there is any debris in there. If it were "blocked", I somehow doubt that the car would run very well, if at all, if it was "blocked." Just to remind you, my car was running extremely well and had no signs of what is often associated with a knackered CAT. It took me a lot of trial and error to get to the root problem and I now wish I had (with hind sight) changed the CAT in the first place instead of investing time and money in trying other parts first kin the hope of saving some money. This I did not achieve. It is easy with hind sight, is it not ????????
I have attached a link to where I bought my new CAT and for information it was £170 , you may also need to acquire a fitting kit which will cost around £12. The supplier of the CAT that I bought does not sell fitting kits but there are plenty on Ebay.
With both the CAT and the fitting kit be warned that there are two different ones fitted to 2005 cars. You will need to have established which your car has and it is best to provide your chosen supplier with the VIN No. for your car. There are cheaper CAT`s available on Ebay but you will have to be aware of quality and warranty. I was personally not satisfied with answers to questions I posed to the cheaper suppliers. There again though, I am a great believer in, "You only get what you pay for". I am by no means suggesting you should take the same approach and that of course is, rightly so, your decision to make.
https://www.onlineautomotive.co.uk/car-parts/Jaguar/S-Type/2.5L/Petrol/Premium/Exhausts/Catalytic-Converters/JAG1036H/1/34#
Good luck with correcting your cars problem.
Regards and Best Wishes , John