Webster was formerly the BSA deputy chairman and replaces Graham Beale, chief executive of Nationwide Building Society, who has held the post for the past year.
Webster said: “I feel extremely proud and privileged to be elected chairman of the BSA and I will be doing everything I can to promote the virtues and values of the mutual sector.
“These are tough times for our businesses and for our customers too, but I believe we can look ahead with optimism as the lessons of the last two years have reminded us that big is not necessarily best.”
He added: “There is undoubtedly an expanding space in the market for a trusted, customer-focused mutual business. Mutuals have a fantastic heritage, but we also have the zest and vigour to adapt to 21st century markets and to demonstrate our relevance and uniqueness in a contemporary setting.”
Peter Griffiths, chief executive of Principality Building Society, has taken over as BSA deputy chairman.
