Yes, you can get a mortgage if you are self-employed. You need at least 1 year’s worth of accounts or income declared to the Inland Revenue.
Different lenders have different ways of assessing self-employed income. For example, they can either use net profit for sole traders or partnerships or salary and dividends if you are a company director with more than a 25% share-holding, some lenders use the above incomes plus retained profit in the business. As you can see there are several ways of proving your income and different lenders like to see various different things so best to speak to an adviser who can point you in the right direction and get you the best deal available.