Absolutely! Traditionally, lenders require proof of employment for the past two years, including standard payslips, when applying for a mortgage.
However, in the case of those that are self-employed, lenders will require them to submit other proof of income such as tax returns and bank statements for the past 2 to 3 years.
The lender wants to see that you have some form of income and that you can afford the monthly payments on the mortgage. If you can prove this, then you can get a mortgage.
Apart from your income, lenders may require an above-average credit score or a larger down payment.