Depending on which credit reference agency you use, a good credit score for a mortgage in the UK is anything above 700. Lenders will generally offer better interest rates to borrowers with scores above 700, and those with scores below this threshold may find it more difficult to obtain a mortgage or may have to pay higher interest rates.
If your credit score is below 700, there are still options available to you, but you may have to pay a higher interest rate or put down a larger down payment. You can improve your credit score by paying off your debts and by making sure that all your credit is in order.
The biggest thing to remember here however, is that lenders will not just look at your credit score to determine how risky it is to lend you money, they will scrutinise the historic events that influence the score a lot more harshly than they will the actual score itself.
A higher score does not automatically mean you are more likely to be able to secure a mortgage. It is however a good indicator that you have little or no prior credit issues, this will in turn indicate that you are more likely less of a risk to lend money to and therefore increase your chances to secure a mortgage.
It's important to work on improving your credit score through good financial decisions such as repaying your debt on time and in full, and not living above your means. These factors will not only help you increase your credit score they will also help you get the best interest rate possible on a mortgage.