Customers of the 97 B&W outlets will become Britannia customers from 3 July.
In 16 locations, B&W and Britannia both have branches within a mile of each other – Britannia is planning to close one of them in each spot.
Leeds-based Ptarmigan will seek to reassure consumers as to how their banking will be affected, and will promote the fact that Britannia is investing £17m in new merged branches.
Britannia group PR manager Emma Taynton-Young said: ‘We’re saying “we’ve arrived” and letting customers know that they’ll be served by the same staff as before, but under the Britannia name.’
Britannia paid £150m for the B&W branches, then owned by the Bank of Ireland Group, last year.