Sorry Sylvain, but there's one question I omitted from my previous post. I notice your comment "Plus I do not think I would need a 5.1 system on a daily basis, so I'm a bit lost", so would you consider a stereo-only option?"
Here are some suggestions based on your criteria so far;
If you were content with stereo only, I'd keep your Quads and get something like a Marantz M-CR610, which contains CD, DAB, DAC, streamer, Airplay and an amp in one petite box. The only other component you'd need then is a Bluray player.
You may like to check your TV's outputs if this option interests you. You can either do as I used to do with my previous amp: providing your TV has a stereo RCA output, you can plug this into the back of the Marantz. Any HDMI components go into your TV. I found this worked very well with no lip-synch issues. You could use a digital output of your TV to the Marantz, but I honestly don't know if this may introduce lip-synch problems. Maybe others can clarify, but at least you've got the option.
The appeal of this system is it's very capable musically, so with your TV & music, it'll sound super. This leaves plenty of your budget left if you wanted to swap your Quads in for something that you may find matches better tonally. Also, I know you said you didn't want a separate CD player, but my experience with Bluray players is that although some are quite capable as far as sound quality is concerned, they're extremely slow to respond and clunky to use: much slower in operation than many DVD players in fact, so at least with this set-up you've got a CD spinner built in with no additional boxes.
if you're determined to go 5.1, I'd look at a Marantz NR1604 with some Q Acoustics 2000i Cinema Pack speakers, or there are some decent deals around on the old Q Acoustics Q7000 speakers (not the new Q7000i updated ones). Although these options technically take you over budget, most dealers are willing to do a fair discount if you purchase them all together at the same time. Just add a £100 Sony bluray player and you're sorted. However, although this system won't be awful at playing music, it will be quite a step down from the stereo option above.
Finally, one bizarre left-field option. I would rarely recommend a soundbar for anything really, but if you're after all-in-one sleekness, you could take a look at the Monitor Audio ASB-2 and just add a Bluray player. You have the option of adding a subwoofer later if you wanted. I own a Monitor Audio Radius One, which although I've replaced, have great respect for its musical abilities, so have little doubt that the Monitor Audio ASB-2 has a decent pedigree and is possibly worth a look.
All the above suggestions do depend on how well prices translate across the channel, but I hope this provides some useful food for thought if nothing else. Let us know how your demos and search goes.