I've been recommended these as an up-grade to my old mission 770s
That's a small-ish room for the Mission 770. Do you like the tonal balance you're getting? Reason I ask is that I too used 770's in a similar sized room and the bass was, er, generous! Usually, a smaller speaker would suit such a room better, i.e. give an accurate tonal balance.
Incidentally, are those the original mid/bass drivers in the photo or have they been changed at some point? I know the designer, Farad Azima, was a bit naughty in that there were several iterations of the 770 even before they officially released the Mk 2 model but I don't ever remember a bass/mid driver that looked like that in either the various Mk1's or Mk2's. Certainly the 770 Mk2 had less bass and it was much better controlled.
I'm familiar with the Quad 44/405-2 amp but not the 34/303. I have to say that neither the 34 or the 303 have a particularly good reputation for audio quality (but maybe they have been upgraded at some point?). The 303 is, evidently, good for driving speakers with high impedances, such as the Quad ESL, but not so good with lower impedance speakers due to the amp's high output impedance which means the damping factor is poor by today's standards. Speakers whose impedance dips to low values in the bass region - a not uncommon scenario - would not be best suited as regards sound quality.
If you really wish to spend up to £10k, I'd look at replacing the amp as well. When I upgraded from my 770's, I chose a sealed box active design. You are in the perfect position to switch to an active setup (i.e. you have speakers you wish to upgrade + a power amp that's possibly out of it's depth).
Agree with SickSquirrel about using a sealed box speaker in your room as it's going to be placed so close to the rear wall. If you chose to go active, then how about these active speakers:
We fire up the latest model in Unity Audio’s geologically themed monitor range to find out just how much it rocks!
www.soundonsound.com
They’re designed to work hard, but these speakers can have a little fun too.
www.whathifi.com
There are many, many other active speakers/monitors available in you price bracket.
But if you wish to stick with the traditional, (nothing wrong in that) how about this:
ATC’s ‘artisanal’ approach to monitor design pays off handsomely with this classy new speaker and amplifier combo.
www.soundonsound.com
...though it will need a good amp to drive them.