It's tricky - there's an over-the-top Scottish accent, which is fairly easy: once you've got that, you can start toning it down.
Just half-roll your "r"s, round off your "l"s and elongate your vowels (especially the "oo" ones).
I've been speaking in an Irish accent for a couple of months on and off, just to see what it's like (and because it's beautiful), and now it's taken over: my Scottish is terrible again! People have been fooled by the Irish though. I just heard some in a Sharpe episode and tried it out - you jut have an affinity for some accents.
I'm English... Don't like saying British, as I'm clearly not Welsh, Scottish or (sadly) Irish, though I can do all the accents. The American accents are fun too: Deep South's the easiest, but Boston and New York are quite good too. Russian is also fun: just turn your "l"s into "w"s and speak at the front of your mouth.