as far as i've been aware, alms house in jamaican/dancehall parlance has had the same meaning for the past 15-20 years and always means, as someone pointed out, roughly 'beef'. or conflict, fuckery, or any other general kind of badness, aggression or front. it's a very vague term.
e.g. 'i'll bring alms house to your mums house' just means i'll come round to yr mum's and be generally annoying, lairy, possibly violent. similary 'don't talk almshouse if you can't back it up' or whatever the dizzee quote someone mentioned earlier is.
nothing at all to do with arms, though maybe londoners have misheard it and assumed that it's about guns, i don't listen to much grime so i don't know.
i've no idea why it came to mean this at all though, from the original meaning of alms for the poor and all that.
...also as tactics points out, many many of these terms are well old and were not originated in grime, or even the uk: kotch, link, still, pickney, shotta, sket/skettel, gallist, don, bow cat, sekkle/settle and bare (actually a corruption of pure as in 'it was pure madness' or 'there were pure girls in there' - becomes 'pere' in a JA accent then corrupted to 'bare) are all jamaican patois (though some, like skettel - biblical term - are older and/or english in origin)
er... I dont think so. Theres that Capleton LP 'Alms-House' for a start... I reckon Demon (or whoever started using it first in grime) either punned it or misheard it.