I have a slightly off-the-wall suggestion; wander the malls.
I was told the same, but about 2 months in I was in Morrisons and Barclaycard reps were there at one of those stands; I filled in the application being totally honest, and was given a card about 3 weeks later, with a £300 limit. I got to increase it to £600 3 months later, and no problems since.