I recall reading it at one point suggesting yes, but haven’t been able to find it in searches. It was a preliminary issue hearing, not one to decide the substantive case. Are these decisions normally reasoned and published?
Casamitjana v The League Against Cruel Sports  UKET 3331129/2018 (21 January 2020) was a preliminary hearing on this issue; that is, prior to the determination of the actual dispute between the parties, there was this decision to the effect that
Ethical veganism is a philosophical belief which qualifies as a protected belief within the meaning of Section 10 of the Equal Act 2010 [sic]
The reference should of course be to Section 10 of the Equality Act 2010. The judgment describes the claimant's actual beliefs, the relevant case law as to the test, and finally in paragraphs 33-39 the conclusion as to why the claimant's belief met the standards.
This decision is not precedential, and the conclusion was not really in doubt since vegetarianism has long been cited as a core example of a protected philosophical belief (that is, a belief other than a strictly religious belief, that nonetheless qualifies for the same kind of protection afforded to religious belief). In terms of the Equality Act, it means that various kinds of discriminatory or harassing conduct are prohibited, in relation to treatment of ethical vegans.
The claimaint, Jorge Casamitjana, worked for LACS as its head of policy and research. He objected to investments by its pension fund that he considered unethical. He was dismissed by the charity, and his claim in the employment tribunal was that his dismissal had been on the basis of his vegan beliefs, amounting to discrimination in violation of section 39(2)(c) of the Equality Act 2010. They later reached a settlement; a brief consent judgment is available. Part of the agreement was the concession from LACS that "we now accept that Mr Casamitjana did nothing wrong" with the way he communicated his concerns to other employees, and they have adjusted their pension scheme.
The case reference is not too difficult to find, after (1) searching for "ethical veganism protected belief" showed the names of the parties, and then (2) "casamitjana lacs employment tribunal" had the judgment as the first hit.