This can be a bit of a grey area. In fact, in normal circumstances it is unlikely that either of your countries of citizenship would refuse help. The country that you are in, however, might insist as regarding you solely as a citizen of the country that you presented yourself as being on entry and so (for example) deny officials of the other country consular access to you if you were in prison. (The country that you used in your example, however – the UK – would not normally do that.)

Note too that if you were simply seeking routine consular services from one of your countries of citizenship while you were abroad (e.g. to renew a passport), then the passport that you used to enter the country you are in is of no relevance whatsoever (assuming, of course, that both the passports are legally held and you are indeed a citizen of both the countries).