After you updated your question, I think it can be boiled down to "Did
the Palestinian mandate end?" The answer to that question is yes, it
did. Albeit obviously not amicably. From
Termination of the British Mandate for Palestine
written in early 1948:
It was in reply to questions touching on the legal
considerations outlined above, raised in the debate on the first
reading, from both sides of the House of Commons, that the
Attorney-General made the position of H.M. Government clear. There was
no general rule of international law, he suggested, to prevent
termination of the mandate by the United Kingdom, and insofar as on a
narrower view the original mandate might be regarded as a kind of con-
tractual undertaking, the impossibility of performing the object of
that undertaking, as originaly contemplated, frustrated the agree-
ment (ad impossibilia nemo tenetur).
In this the Attorney-General was of course directly in line with the
report of the United Nations Special Commission on Palestine which in
its comment, appended to the first recommendation that the mandate
should be terminated, stated inter alia:
'In the nature of the case, the mandate implied only a temporary
tutelage for Palestine. The terms of the mandate include provisions
which have proved contradictory in their practical application.'
"ad impossibilia nemo tenetur" states that no one is required to
perform the impossible. If governing Palestine was impossible for
Britain, it had the right to stop trying. In addition to that, the
United Nations Special Committee on Palestine
supported the termination of the mandate:
It is recommended that
The Mandate for Palestine shall be terminated at the earliest practicable date.
It is recommended that
Independence shall be granted in Palestine at the earliest practicable date.
Note also that in 1948, the mandate system had already collapsed and
all other remaining mandate territories had become
United Nations Trust Territories (the sole exception was South West Africa, modern day Namibia, which survived as a mandate until 1966).
For your other question, whether Britain held sovereignty in Palestine
or not. The answer is that they did not. See for example
Some Legal Aspects of the Mandate System: Sovereignty: Nationality: Termination and Transfer where that question is discussed extensively.
Edit: I found the following written in an essay called Israel's Borders under International Law by Anthony D'Amato
Is the Palestine Mandate still in existence? I think it is. Although the Mandate was dated to expire in August 1948, an essential term, namely the creation of an "Arab state," was not fulfilled. Of course this was the fault of the neighboring Arab countries, but one still has to protect the beneficiaries of the trust, namely, the people living in the area. The Jewish people were protected by the creation of their state, but the Palestinian people were not protected. Therefore I would argue that the Mandate survives until its substantive terms are fulfilled. The most important substantive requirement still unmet is the creation of an Arab State (Palestine).
I first discarded it as hogwash because of the crappy layout and strange abstract ("I am not a Jew. I am not an Arab. In trying to assess my internal biases...") But then I googled his name and Anthony D'Amato is apparently a law professor, teaching international law and human rights. So if a law professor says it exists, perhaps it does! Then it is not unreasonable to think that Britain is still the Mandatory Power.