Jaguar Forums - Jaguar Enthusiasts Forum - Suspension issue? Opinions please

So, I've had my first ever jag for a couple of months now and it recently passed it's MOT. (Yay..!) The guy who inspected it went over the obvious suspension parts with a crowbar, bending and pulling to check for any slack, but it seemed Ok.

However, I have noticed this weird sensation when accelerating. It's almost as if you're going sideways. It feels like it's floating a bit and it has scared me a couple of times while overtaking. It can suddenly pull into another direction and I have to adjust the steering rapidly. I scrapped the old tires but noticed they had uneven wear. The inside of one of the rear wheels were worn down. Normally I would have just taken it to a garage for a new alignment but I found a receipt that showed it had already been done.. at least some 2 years ago.

Could this be an issue with bushings in the rear suspension? I've noticed some similar threads on this forum, and changing into poly urethane bushings seems to cure the problem. But I don't really want to go that way unless I know for sure.. It looks like a hell of a job. So do you have any opinions?