Not a combi boiler (3 storey house), but no tank either so it must be mains fed.
not quite sure how that follows… where is your hot water coming from? If it isn’t from a combi boiler, then it must be being heated in a tank.
Have you got an unvented (aka mains-fed, direct) hot water cylinder and no cold water tank?
If you have, then you won’t have the dead pigeon issue, but I’d still not fancy drinking the water, since it will have been held in a ‘hot’ / ‘warm’ state for ages breeding bacteria.
From a ‘let them eat mud’ perspective, you’ll be fine 99.99% of the time, but occasionally you might get some nasty bug, like legionnaires disease 😕
Dave