titchy77 congratulations!
You don't have to tell your employer until you are 25 weeks pg although most people do before then. The probationary period is a bit of a red herring, it's not a legal concept and in normal circumstances a new employer could get rid of you within a year quite easily regardless of whether someone passed their probation or not.
However if they sack you because you have told them you are pregnant that is unfair dismissal and sex discrimination. So they are unlikely to do that - from that point of view they are probably less likely to get rid of you if they know you are pregnant than if they don't!
I'd wait until you've started at least. You may choose not to say anything until 12 weeks, as lots of people do. I think most people tell their immediate boss earlier than that, sometimes you might be very tired or have morning sickness particularly during the first trimester, so it may help for your boss to know.
It doesn't need to be a problem, you'll still be there for quite a while yet, you have time to make a good impression, make progress in your new role, help plan for your maternity leave and set yourself up to be welcomed back with open arms when you have finished your maternity leave.
I don't know what the maternity policy is with the NHS, you will need to check that, but you won't be entitled to SMP as you won't have long enough service. Check whether the maternity pay at work has the same conditions attached, you may be lucky, or see here about Maternity Allowance which you may be entitled to instead.