Most mortgage lenders will want to see at least two years trading figures, a few may accept one year but this will be reflected in the rate they offer. There are secured second charge lenders which will accept borrowers who are only self-employed for 6 months and they will offer a self-employed secured loan at their lowest rates.
Of course income proof is still important so make sure you can provide your accountant with trading figures as he will be asked to provide a projection for the first year. Dependant on the type of your business there is other supporting information which may help. Talk to a loan adviser to find out if you qualify.
Please note: If you are a contract or agency worker you may technically be self employed. However, unlike someone starting from scratch in a new business you are likely to have a track record and income receipts in the same line of work but with different firms. If we can demonstrate that track record to a lender, accounts or projections may not be required.