I would ask the shop for more details, especially regarding the vague "something from the motor". Kinda sounds like scare tactics. All cars leak oil.

If oil consumption is normal, you're not seeing any stains where you park, or noting any burnt odor while driving, I'd suggest monitoring the situation for now. Check the oil level every few days as a precaution until you know the engine is not suddenly using lots of oil. If you do see oil collecting under the chassis, you can always look into it further. If repair is warranted, I'd suggest finding another shop with less intimidating business practices.

Keep us posted.

 

The under engine plastic tray can hold quite a bit of oil from the engine before it drips on the ground.
A couple of common small engine oil leaks are:
Sump drain plug sealing washer, I recommend changing this every time you have an oil change. (Part number NCE1859AB £4 + from jaguar, or complete sump plug JZH100062 £8.37 + from Jaguar.)
Oil filter, some oil filters have been known to weep oil from the where the can joins the base. (The Jaguar item is C2C41611 and costs £13.60+ )
There are obviously many others!!
Mellow

 

I would recommend removing the under tray and cleaning up the suspect area with a suitable solvent. You can then see the source and monitor the volume of the oil leak. It may be as simple as sump bolts that need to be snugged up...

Modern Jaguars do not leak like their XK engined predecessors, which had drip pans under them when sitting nrand new on the showroom floor.

 

I agree with the above approach, that is what I would do as well.

However it should be noted that my XJ40 with its AJ6 engine and 140k + miles had no oil leaks, apart from when the cam cover gasket split with age!
I worked on these cars about 25 years ago now and oil leaks were not an issue on the XJ40's. That is apart from the classic head gasket leak caused by poor factory assembly damaging the oil seal, but once the gasket was replaced they did not leak again.
But I do agree the older cars with the XK6 engine dating from 1949 and used up to 1986 in the Series 3 and up to 1994 in the DaimlerDS420 Limo. did have oil leak issues!

Mellow

 

Oil Leak Reason and fix. Read Here

 

Those XK engine oil leaks were actually factory chassis corrosion protection...

 

The OP never did come back and tell us what the source of the oil leak was; he has been MIA since March 2020, so I suspect he won't be able to take advantage of your post and link...