You may be interested in more informal chess and there are currently these weekly opportunities:

Tuesday Ludo Lounge, Southbourne Grove, Bournemouth 2.30pm to 5pm
Wednesday Flirt Café Chess Club, Bournemouth 2.30pm to 5pm
Wednesday Amberwood Inn, Walkford around 8pm
Thursday Cafe Tratt, Swanage, 10.15am to 12.15pm except in winter, when it moves to Chococo at the same times.
Thursday Highcliffe Community Association Greystones 1.45pm
Thursday New Milton Conservative Club, 24 Station Road, New Milton, 2pm to 5pm
Friday Royal British Legion, Wimborne from 10am
Friday The Crooked Book, Boscombe 11am to 1pm

There are typically no board fees, but chess players are expected to buy a drink, i.e tea/coffee/soft drink or something to eat