Yes, you can - and I'd suggest you try Bristol and West. They have mortgage plans specifically aimed at people with credit problems - you pay a small amount above the odds for a few years, but if you operate the mortgage properly then they will move the interest rate to their "ordinary" rates.(posted 8279 days ago)I remortgaged with them a while back as I was sick and tired of the Halif*x (hard to believe, I know). B&W were very helpful - I was completely up-front about my difficulties and they allowed me to remortgage without a problem.
When I was chatting with the lady at B&W she said that what they look for is honesty - if you're up-front with them they'll help you, but if you try to conceal your credit history then they're less likely to help.
Hope that helps