I do think you'll find it pretty hard. My OH was refused a credit card for one single default in his whole life....and it wasn't really a default, it was a dispute (all sorted now)
I'm not sure how much lenders can see about your credit report but if they can see you owe HMRC it might be a big fat no, or you'll be paying way over the odds.
When you say a steady job, how long have you been in this steady job?
If that is the assessment you have received from the tax man then you are very lucky as I did some calculations and they come out a lot more than that with penalties!