I should have put this in my post.
I have to tell them at some point so I can arrange paternity leave. In the UK you have to have worked for your employer continuously for at least 26 weeks by the end of the 15th week before the expected week of childbirth to get paternity leave[1], and holiday allowance for new employees is usually pro rata based on number of months worked, so I won't be eligible for paternity leave or have much holiday allowance by the time the baby is due. So before I accept an offer I need to know that they will be flexible about taking unpaid leave.