Staff from Lloyds TSB are to ask customers to sign a petition against the bank's plans to transfer some of its operations to India.
Staff at branches in Hampshire will petition customers
Members of the Lloyds TSB Group Union will ask people at branches in Fareham and Andover in Hampshire, to also sign a letter to the bank's chief executive.
The action follows the bank's decision to open a call centre with 150 employees in India.
About 107 jobs could go from offices in Bournemouth and Newport, South Wales.
Steve Tatlow, assistant general secretary of the Lloyds TSB Group Union (LTU) predicts up to 40% of the workforce across the UK could lose their jobs if call centres, service centres, which deal with administration, and IT services are transferred.
He said: "If 90% of customers are against the move, I do not think the company is going to be able to ignore them.
"The bank then risks losing its customers. The letter to the Chief Executive Eric Daniels says: 'I do not want my account to be handled abroad, I want it to remain in the UK'."
The union, which has collected 260,000 signatures so far, hopes to increase that figure to 500,000.
People entering and leaving the two branches on Monday will be petitioned, along with Lloyds TSB account holders in Edinburgh, Newcastle, Newport in South Wales, Newport in Plymouth, Southend-on-Sea, Peterborough and Gloucester.
The action comes on the day the bank published record annual profits of £4.35 billion.
A Lloyds TSB spokeswoman said: "In September we announced our intention to have 1,500 roles in India by the end of 2004.
"Of this 1,500, there are already 250 roles in India. We have announced that a further 750 roles will be from a call centre in Newcastle and 150 from General Insurance, which leaves only another 350 roles.
"It is too early to say where these roles might come from but we are committed to keeping staff and customers fully informed of the process."
Mr Tatlow said the union, which represents more than 45,000 staff, is also lobbying MPs, MEPs, the Scottish and Welsh Assemblies and councillors in a bid to halt jobs being exported.
"We will fight on until we succeed and we have every confidence we will succeed, " he said.