I'm just about to collect a 2007 XK convertible that was re-imported from Ireland in 2015. It is claimed to have very low mileage - 15,000, but not supported by any history. 

There isn't time to try to check with JLR HQ in Ireland before I go. I've never owned a Jaguar before. Apart from the usual stuff - driver's seat cushion and bolsters, pedal rubbers, steering wheel and gearknob - is there anything else I could/should check that might be a giveaway of higher mileage than that shown?  

You could try typing in the reg number into DVLA MOT History website https://www.check-mot.service.gov.uk/  as this shows mileages between MOT tests

That is assuming any info exists for it with DVLA being that its from Ireland...sorry, know very little about Irish registered cars

I already have the DVLA UK MoT history, but there's only two tests - 2015 and 2016. 

The Irish test - NCT (National Car Test) is biennial, but they will only only release info (including mileage, or in their case I suppose it should be kilometreage...) on test results to the registered owner on the date of the test. No hope there, then.

I'll try Jaguar HQ tomorrow to see if they can put me in touch with the Irish equivalent to try to get the service history, if any, which would of course have the mileage.

So far as the car is concerned, I have no trouble at all in believing that it has only done a very low mileage - very slight signs of wear on the steering wheel, virtually no wear on the pedal rubbers, no sag in the driver's seat, no sign of wear at all on the light-coloured leather gear lever knob. The paintwork needs some attention, as do the wheels, but I reckon it's a good 'un. It's definitely a keeper.