There is an option available to you - a self certified mortgage.
This is where you declare your total income without proving it - no payslips, bank statements and so on required.
A larger deposit is required, which you have by way of equity in the property, and a higher rate of interest is normally charged.
I would not usually advise such a mortgage, but needs must and I think for such a relatively small mortgage and your needs then it is worth considering. Bear in mind that after a year or two, you will probably be eligible for a 'standard' mortgage at a better rate, so be sure to check for any exit fees, redemption fees or any type of fee for switching within the first few years. Make sure such a fee is reasonable.
Self certified mortgages can still be variable, capped, fixed rate and all the other options that are available with standard mortages.
As always, be very sure you can afford the repayments plus 10% comfort zone in case of rate rises and so on.
Do not take the first mortgage offered. Try at least three different places. I hope your ex will be understanding and allow you the time you need to find the right mortgage.
Good luck