2001 740i (E38) MOT failure - rear bushes

Hi Guys,

I have a 2001 740i (facelift E38), it has 110k miles on the clock. I just had
it MOT'd today, and it failed on both rear suspension arms having
excessive play. Here is what it said on the sheet:

01 nearside rear upper suspension arm has excessive play in a pin/bush
02 offside rear lower suspension arm has excessive play in a pin/bush

I wasn't able to speak to the guy in person, as the MOT was done via a
pickup/drop-off service, but I called him once I got the car back. He just
basically restated what it said on the sheet, and offered to show me
exactly where the problem was if I came in in person. I will do this
tomorrow.

When I got home I jacked up the back of the car and took the rear wheels
off. They had no noticable play. I have given all the suspension arms a
good pull in all directions, and there was no apparent loosness or
movement that I could detect.

Has anyone got experience of this? I just can't figure out what the
problem is. I can't find anything loose back there. I knew that at that
mileage, the suspension may be a bit worn, but it looked pretty pristine,
and there was no sign of wear or damage.

Any tips or advice? What is this likely to cost to resolve? i am happy to do
work myself, but don't have access to proper garage equipment. Can I DIY
the repair, or is this a bmw specialist job?

To make things worse, I'm selling the car at the moment, and wasn't
planning on having a major bill to pay.

Thanks for any advice,

Robin