First time mortgage, new job

[Deleted User]

Looking at buying a house for the first time, on my own.

Just finished a 2.25 year contract on a bit under £40k/year. Got an offer (pending pre-employment check) for a new role on bit over £40k, 6 years (technically still temporary!?), with 6 months probation. Aiming to start early September, so I have a few weeks "off" inbetween. My credit rating is pretty good I believe.

Thinking of a house around £160k, £23k deposit, so want to borrow £137k (just over 85% LTV - would slightly under be any better?).
Under 3.5x salary, so significantly below the often quoted 4.5x salary max.

Now if I waited until my probation period was over, I realise I'd be in a pretty good position.
I also realise that in the gap between jobs with only an offer letter, I'm not in a good position.

However what I'm wondering is can I go for a mortgage with a single payslip at my new job, i.e. still on probation?
I'm assuming I'd need to speak to a local broker, and not an online-only one, to find which lenders actually allow that?

I don't really want to wait until 2020 to get things moving!