1994 Jaguar XJ6 smoking on start-up

I doubt the explanation of fiber seals, but I do agree on the leakdown of oil into the cylinders. It's most likely caused by a sticking valve that's not fully seating. Cars that sit for a long time tend to develop this problem.

I'd start by changing the oil and then regularly driving the car every day (cold to fully warm) for the next week. Try to get at least a hundred miles on the car. If the problem doesn't disappear, you'll want to do a compression test to see if you've got a leaking cylinder or a blown head gasket.

Speaking of head gaskets, check the area around your oil dipstick tube for errant oil. If you find the area covered, you'll want to do the compression test right away.