I can definitely say within 6 months if you're working a nice job.
I moved here 1st February, worked temp, but didn't get my present position until 1st June. I was shopping in Debenhams in July, one of the clerks offered me an application for a store card. I told him at the time I didn't think I would be accepted, but he said give it a try, so I thought why not.
I didn't fudge anything, he asked my residence address, how long I'd lived there, my job, how long I'd been working there, where I worked before, where I'd been living before February. I told him at that time Sweden, gave my residence address in Sweden. He stuck it into some kind of machine that read it, I assume, and then told me I was being issued a Debenham's card with a £250 credit limit. Okay, whatever.
I have to say that given that, when I was asked a few weeks later at BHS if I wanted a store card, I thought why not (although I seldom shop there), but I didn't get the card, same procedure.
Then in August, I was asked at Marks & Spencers and I do have to say I DO do quite a bit of shopping there, and it wasn't for a store card per se, but a M&S Mastercard. I didn't realize that when I was applying, once I found out, I thought for sure I would be turned down, I mean it's a Mastercard already, but about 2 weeks later, there's a Mastercard in the post and I have to say, the credit limit is in the low thousands, not hundreds.
That being said, I do NOT buy often on credit and my Mastercard is used only for things like plane tickets home and theatre tickets when my husband came to visit from Sweden, but I also throw a few hundred at it, not the minimum payment either, but the fact remains, I have a real credit card and I have only been working my full-time job since 1 June and have only lived here since 1 February and I don't have a husband living here either. I'm also not a stockbroker or anything like that, I'm a legal secretary working in the City of London, which is admittedly a pretty well-paying job, but still ....
So that's just one person's credit story, for those who ask how long it takes here in the UK.