I took out a second mortgage recently with the same lender as my original mortgage. However, in the meantime I had taken redundancy and set up my own business - a limited company with less than two years finalised accounts available (I'd only been trading 23 months). Mrs Q had also changed jobs and only had a few months payslips. To make matters worse we were spending like water doing up the house (hence we needed a mortgage!) having had an extension and planned kitchen refit so our spending history needed a lot of explaining. It all took forever.
The bank were reasonably considerate of how our finances work - but as a company director I pay myself a paltry basic salary and top it up with dividends but of course the dividends are not guaranteed (even though the company is just me!), don't show on your P60 etc.
I thoroughly recommend sorting a mortgage out before you leap into the gig economy. The banks are really set up to assume you have a "proper job". As a minimum, expect to provide your last P60, three months bank statements, three months pay slips and a breakdown of your monthly expenditure including details of any other loans, overdrafts, HP agreements, maintenance payments etc. They will be keen to understand your actual ability to pay.