I don't know anything about birds, the bad one was black with a red
crest and a longish beak,

Most woodpeckers have red feathers on the head but if, as you say, the bird
was black then it might have been a dyocopus martius a.k.a. a black
woodpecker but they are almost as large as a crow and have not been recorded
in Britain. Stand by for twitchers?!!

My guess is that it was either a great spotted woodpecker (picoides major)
which also has a red bum or a lesser spotted woodpecker (picoides minor)
having no red bum! Both these are fairly common and the former has a
penchant for bluetits' peanuts so it might be an idea to move any peanut
dispenser far away from any nest box.

By the way, the best thing for getting rid of blackfly etc from your roses
are peanuts. Use a plastic container (dried milk type are best) cut a 2
inch diameter hole in its base place a piece of wire netting (the sort used
for peanut dispensers) inside the container so that it covers the hole.
Fill up the container with peanuts, put the lid on and hang the container
not too far from your roses. Whilst the bluetits are queueing to get to the
peanuts, they do the rounds of the roses and eat the blackfly!

Geoff