In this case, I think definitions 1& 2 apply (repeated here for reference):
1.Used to show spoken words
2.Used around odd or unusual terms, jargon or slang.
Looking at the linked linked by the BBC, we find the following:
"Will the vaccines work against the new variant?" (Headline)
"even though part of the spike has mutated, the vaccines should still work." (in the article)
So definition 1 applies
I do not think "work" is a term of art in the field of vaccine development.
In the linked article, the term "vaccine escape" appears three times. This term would appear to define what would be necessary to the vaccine to cease "to work"
In an article in Nature we find some other terms that are, I think, relevant.
https://www.nature.com/articles/d41586-021-00031-0
Here it is stated that a vaccine may be "compromised,"
that the mutations may "diminish" the potency of the vaccines
that the "effectiveness" of the vaccines may be "diminished"
that the "mutation shared by both variants did not alter the activity of antibodies produced by people who received a vaccine"
that the "{mutatant] variants could weaken immune responses triggered by vaccines"
that "the [research] team found little difference in the potency of antibodies generated by 20 participants against viruses carrying the N501Y mutation, compared with viruses lacking the change."
that "the 501Y mutation, at least, did not drastically affect the activity of neutralizing antibodies in convalescent serum"
that " the 501Y mutation is unlikely to alter immunity"
The phases quoted above focus on identifying reasons why the vaccine might "not work" and the BBC by using "work" (in quotes) is their attempt to show their story summaries their understanding of all of this evidence against a worrisome "immune escape" by the mutant variant.
Finally the following comment "Moderna . . . which has developed an RNA-based vaccine, has said that it expect its jabs to work against the UK variant" uses some informal language ("jabs")and leads us back to the idea that the quotes in the BBC piece are a direct quotation of someone.