Sounds kinda dumb but have you tried lubing it with something like WD-40?
Then working the handle a few times. Some won't like WD-40 but you can use what you like.

Post some picture of your car, we don't see many members from Sweden!
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Well it's just a door handle and I can't see any kind of lubricant hurting anything?
Maybe you will need to wipe the door down afterwards?
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Thank you. Photos uploaded . The photo with the two Xj's, mine is the one far back. There are only 186 of the new generation (2009--) here in Sweden so imagine how extremely surprised I was to out of nowhere see a white XJ with the same exterior spec as mine.

 

This happened to one of my rear doors, and there is a technical bulletin describing how to resolve it by using a knife blade to shave part of the internal moulding off which causes it to rub and bind. I note it appears cold in your video which was when mine starting binding too. TSB and workshop steps are attached. Removing the handle is easy (just one screw on the door jamb) but note you do not fully remove the screw only loosen it as shown in the instructions. Also pay attention to locating the connector into the slot correctly if you fully remove it. (You can shave off the moulding without fully removing if you have someone else to hold the handle. You do need to remove the fixed part first though.)

NB don't use any kind of oil or grease on your door handles or latch mechanisms - they will attract dirt/dust which will block them. Only use dry lubricants, e.g. a Teflon/PTFE spray.

 

 

Xdave comes thru again!
Thanks much for the real answer.
If you don't work for Jag they should pay you anyway!

Vika01 please post back if this got you fixed up?
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WD-40 didn't seem to work. Will see tomorrow if it's settled and maybe made a difference.