However, as AIMS points out in relation to the 1907 Notification of Births Act, found here: http://www.legislation.gov.uk/ukpga/Edw7/7/40
"it shall be the duty of the father of the child, if he is actually residing in the house where the birth takes place at the time of its occurrence, and of any person in attendance upon the mother at the time of, or within six hours after, the birth, to give notice in writing of the birth to the [Registrar] .........."
The Births and Deaths Registration Act of 1953 is quite clear:
"The following persons shall be qualified to give information concerning a birth, that is to say—
(a) the father and mother of the child;
(b) the occupier of the house in which the child was to the knowledge of that occupier born;
(c)any person present at the birth;
(d) any person having charge of the child."
The Act can be found here:
http://www.legislation.gov.uk/ukpga/Eliz2/1-2/20
Basically, the notification of birth is usually signed by the attending midwife and this automatically alerts the registrar and the parents turn up some time later and sign and collect the baby's birth certificate. So it is a 2 phase process - notification and later registration, either of which can be done by the father. A letter notifying of the birth should suffice as this is essentially what has passed between hospitals and registrars. Of course nowadays it is all automatic via computer link but that is not a pre-requisite for registration.
The NHS number is issued as part of this process but the LSAMO (see website below) should be able to obtain an NHS number for the baby if the midwives will not oblige. http://www.lsamoforumuk.scot.nhs.uk/
So the NHS number is really a separate issue and can be dealt with over a period (hospitals have a way of accessing an NHS number in an emergency e.g. for visitors arriving from overseas and being rushed straight to A & E with a DVT for example). My advice would be:
a) see if a local midwife or Supervisor of Midwives will notify the birth if you are happy to contact one within the 6 hours mentioned (this will sort the NHS no issue too); or
b) write a simple letter to the local registrar advising of the birth (date, time, sex etc); and
c) wait a week of two to see if the registrar writes back and then visit to register in the usual way. In theory you should be able to sign the register and obtain a birth certificate; and
d) ask your GP or health visitor to sort out the NHS number or contact the LSAMO.