@boromu222 the British Immigration authorities may be alerted and wish to check a person's other nationalities if something nefarious is suspected, but the Passport Office simply issues passports on the basis of eligibility.
Immigration, Nationality, and passports are three completely separate bodies. There is sometimes crossover, but dual/triple/quadruple nationality obtained legally isn't an issue for the UK and no questions (other than the pro forma "do you hold another nationality?" question on various forms (and this, for passports, is more to ensure the person requesting the passport can travel on their other document while they wait for their UK one) would ever be looked into.
That may be different of course in other countries, many don't allow dual nationality, but the UK authorities (all things being equal= unless it's suspected that one or more of the docs has been obtained fraudulently or erroneously) will not comment on that, because it's not relevant.
Pps are correct- technically there is nothing to stop you entering and leaving on different passports. Practically this may have repercussions (stamps, resulting as overstaying when that isn't the case etc) but technically, it's fine.