The 671 is really a side ways step from your current receiver and the 771 is not going to be a huge upgrade in terms of sound quality. With either of these receivers all you are really going to get is more features i.e. 3D you are not going to get a real improvement in sound quality. Also, although your speakers will work OK they are not going to get anywhere near the best from your new receiver (you are not getting anywhere near the best from your current receiver either).
If you want an improvement in sound quality I would say you would be better spending your money on new speakers and not a new receiver.
I hear what your saying PSM1 but my Onkyo has that HDMI issue which i'm sure you've herd about (no more Onkyo's for me) didn't even last two years before it started plus for size reasons my bostons are just great for what I need.
Maybe one day I will in future upgrade my speakers (maybe when kids get bigger) but for now just want to get a decent amp that will last longer than two years plus I got a 3d tv which is next to useless for games whith my Onkyo.
What speakers would you of suggested anyway PSM1 bearing in mind size and everything.
I would look at the Monitor Audio HD range or Kef 2005 as a good place to start.
THe other option would be to save a little money and go for the Yamaha 471/571 instead or even the Denon 1912 which is the same level as the 671 but only £300.