Originally Posted by Confus

You’d have to call to book but I very much doubt there would be a fare filed that would allow what you’re after, so it would likely have to be a complicated construction of end-on components. Don’t expect a pretty cost.

Originally Posted by eefor jfp

As far as I know, this is not possible. Fares are coded/purchased so that the same fare basis is for one direction, so that you could do, for example, LHR-DUB-SFO in biz and then SFO-DUB-LHR in Premium Economy. But you can't but separate legs in different classes in one direction of travel.
The way around this is to upgrade the legs after you buy them, either online via a POUG or at the airport at the desk in T5A (works for the legs from London but not to London). Or you can upgrade with Avios but then you don't get the desired tier points. There are threads on POUGs and upgrading but since I've never done it, I can't be of much help. Others, I'm sure, will be more versed in the steps you need to undertake.