The main reason why someone who is self-employed doesn’t have accounts is they’ve only just started working for themselves and haven’t filed a tax return yet.
A self-assessment tax return is due by January 31st following a tax year-end (5th April). For example, if you started working for yourself on 6th April 2019, you wouldn’t need to do your first self-assessment return until 31st January 2021. That’s almost 22 months after becoming self-employed.
A limited company is required to submit a corporation tax return nine months and one day after the end of the accounting period for the previous financial year.
That said, you don’t have to wait until the deadline to file a tax return. Filing a tax return earlier could mean that you have one year's accounts evidence of earnings for lenders.
This means the first tax year of being self-employed is the most difficult for someone to get a mortgage.