Once you are an affiliated member* you are permitted to enter tournaments taking place in Dorset and beyond (unless they are restricted to that other county).
Most local tournaments are set up and arranged by the Dorset CBA (County Badminton Association) or by the BPC (Bournemouth Performance Centre), although there will sometimes be others available to enter.
Please follow this LINK which will take you to the tournaments page of the Dorset Badminton website.
*as long as you have joined Badminton England you can enter tournaments. If you only plan on entering the occasional tournament then there will be a £2.50 fee per tournament levied by Badminton England. If you plan on entering lots of tournaments then you may prefer to pay a little extra for the “compete”* membership from Badminton England, in which case you will not have to pay the £2.50 levy per tournament.