Box of Tricks

Without any actual research and only a few years working for an Archdeacon, my take on the funeral would be:

You could have the Bishop of Fulham presiding over the funeral if the dead person was really, or at least quite, important. Alternatively, if the dead person or a close member of the family knew the Bishop as a friend, he could be asked to do so. This is certainly the case with Archdeacons (I'll e-mail you about that separately). However, this would need to be in the Bishop's own clerical jurisdiction, ie, within his own See. He could, if permitted to do so by the incumbent, perform religious services, etc, in another parish. There are courtesy "rules" about clergyman taking services in parishes other than their own.

As far as the post-war birth certificate is concerned, there is no mark indicating England, Britain or UK. (I'll send something over by e-mail). The certificate is entitled: Certificate of Birth (or Certified Copy of an entry of birth) Pursuant to the Births and Deaths Registration Acts, 1836 to 1947. Boxes completed include: Registration District, Sub-district and County. Nowhere on either an original or copy is the country mentioned. There is a coat of arms. On a "copy" there is mention of Section 8 of the Births and Deaths Registration Act 1874 but that refers to the namne of the child.

I would guess that the references to the Acts of Parliament is enough to show that it's a British birth certificate.