Many of the 20 loss-making outlets may be sold to management buyouts, said John Burke, chief executive, who announced a pounds 7m restructuring provision for the branches in the half-year to June.
But B&W plans to keep its much bigger Hamptons estate agency business, which is a more upmarket operation with 74 offices that has stayed in the black.
Reporting half-year profits before tax and after restructuring costs up 27 per cent at pounds 26m, Mr Burke said the market was still flat and needed more economic confidence to generate activity.
B&W had improved its performance to the point where it was interested in buying or merging with other societies.
Meanwhile, Allied Irish Banks confirmed it might bid for Household Mortgage Corporation, whose institutional shareholders last month appointed Barings to look for buyers.
AIB said it was still examining documentation sent out by HMC, which has pounds 1.6bn in mortgages.
But it may be up against stiff competition because a substantial number of potential bidders have asked Barings for details, including Abbey National, Birmingham Midshires and Leeds Permanent.