Hi

I'd probably get your parents to try UPS or Fedex. Not really that cheap but, reliable.
Parceforce can be a bit ropey though, but I would imagine with what you've said, it would be ?250-300 + insurance.

Or..
I think if memory serves, there is a branch of Mail Boxes Etc in Bristol. They are pretty good for packing things properly and shipping and are usually very good - I use them a lot in the US and they are great.
Perhaps you could get the parents into your local branch and go from there!