Hi Joe,im local to Bournemouth myself so may be of some help with this one even though i dont fish for Mackeral much these days i did spend most of my summers on the local beaches and piers after them a few years ago.
None of the B'mth beaches are amazingly productive for Mackeral,but there not too bad either.B'mth pier is fairly good with feathers,spinners or float gear and you can have a fun few hours fishing from there.
The trouble with most of the beaches is they are really popular sunbathing and swimming beaches,being pretty full with swimmers till late evening.
So try B'mth pier,Hengistbury head groyne,Boscombe pier.
If you can go a little further east you could try Barton or Highcliffe beaches in the evening with feathers,always seem to produce a few macky about this time of year.
But all said and done you cant beat Chesil for sheer number of Mackeral if thats what your after,Abbotsbury,Ferry bridge etc are some of the places you can go to and really fill your freezer with mackeral at this time of year