This is the reply I received today from the Embassy in DC. I have removed their names.
EG
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Had another look at this case and from the information which is provided, i still do not see a case for Registration under Section 4C of the British Nationality Act 1981.
1. Paternal Grandfather born in the United Kingdom is a British Subject by birth under the Section 1(1)(a) BNSAA 1914
2. Daughter born in 1934 outside the UK and Colonies would have been a British Subject by decent under Section 1(1)(b)(iv) BNSAA 1922, as read with BNSAA 1914 (father in diplomatic service). On the introduction of the British Nationality Act 1948, his daughter would then have had a status of British Subject, Citizen of the UK & Colonies Section 12(2) BNA 1948. This is nationality gained by descent.
3. Under the BNA 1948, females could not pass on nationality. However, if they had been able to, her daughter would then be the second generation born outside the UK and have no automatic claim to British Nationality (unless registered at a Embassy within one year of birth under Section 5(1)(b) BNA 1948).
I may have missed something here, so therefore i would advise applicant to go directly to the Home Office with her enquiry as they are the ones who make the final decision. Best sight is
http://www.ind.homeoffice.gov.uk/content/ind/en/home.html Hope this helps