I think that lenders will usually require you to have been employed for at least a year.
I'm not sure that there are hard and fast rules on this though.
Normally they will look for a P60 and 3+ months of payslips.
Or more detailed and historic info if self employed/contractor.
Also be aware of the lending limits/rules that apply these days:
Yeah I've gone over that with a fine tooth comb, this is the last nugget of info I can't get my hands on, I have a part time job and my partner a full time. I just started, she's been at it for years