This is the process I’d go through.
Get as big a deposit off Mrs Matt’s mum as you can – as soon as you can – even if you have to pay back some later. Try not to make it too obvious – but don’t get caught out money laundering or avoiding inheritance tax. (Maybe you sold her a car?) 😉 ) If you have the money well in advance the bank won’t have to add your MIL to the mortgage which will save time, hassle and money.
Make sure your credit scores are good and fix any problems. – Make sure phone bills, credit cards are all being paid regularly and aren’t in arrears.
Get your earning evidence ready. Now is the time to do some overtime.. (I mean a little bit of extra income might help your affordability score – don’t go nuts if it’s unsustainable).
Don’t just choose a mortgage based on the rate, or the fees, or the monthly repayment. you need to look at all of these and the overall cost. at £50k something with low fees is probably most important.
Some banks are faster than others. your bank might not have the best rates – but many offer discounted fees, and they have direct access to your data which saves time and hassle. Worth getting a quote.