If your aim is to rank as well as you can on searches made from the UK (google.co.uk searches - that's the "default google" here), you really need both a UK domain name (i.e. ending in ".uk", not necessarily specifically a ".co.uk") and certainly UK hosting, too. As explained (sort of) by yellow-boy Cutts in the 90-second video just below.

The .ly domain itself is another story again: they may not be too safe altogether (not too surprisingly, perhaps, in the circumstances?): The .ly domain space to be considered unsafe | :Ben Metcalfe Blog

What impact does server location have on rankings? - YouTube

Here's some more information about how Google does Geotargeting with tlds. I didn't watch the video with Matt "yellow boy" Cutts, so I don't know if this was covered.

Basically, .ly is a country coded tld that corresponds to Libya. Unlike some country coded tlds like .tk, .sc, and .ws, which Google can treat like a generic tld, you're going to have more difficulty getting Google to treat a .ly domain like its meant for any country besides Libya.

Unless you're not interested in SEOing the domain, a .co.uk is probably your best choice of a domain for an audience in the UK.