As mjcairney says... a few things... make sure you have a good SCART lead - I'm not saying spend ££s, but try get one that's of a reasonable quality.
Then, in Sky settings - Picture - ensure you have the PAL / RGB selection set to RGB, then ensure you have SCART Control set to On - otherwise you will not have RGB - but Composite going down your lovely SCART lead.
Then, on the telly, make sure you're connected to the RGB enabled SCART socket - a lot of TVs have numerous SCARTs, of course, but often only one (EXT1) is enabled for RGB.
This should be the best picture you will get on your new telly with your Sky+ box... and it should be fine. Very nice in fact.
If you've done all that (except maybe the good cable) then the cable quality is the last resort I guess, but don't go spending £40 or something... a £20 cable (Ixos or something) should be good enough.
The bigger the TV, the more issues you might notice. And I don't believe you tell us the size of TV... is it a 32" or a 50"? My Sky+ looks very good on a 46" connected via RGB SCART.
Cheers, DpM