In a separate move highlighting this expansion, Britain's phone-banking pioneer First Direct is about open a second call centre, to deal with its increased workload.
The new operation in Glasgow will operate alongside its existing centre in Leeds, which was founded seven years ago.
According to the research by Datamonitor, a management consultancy firm, just 10 per cent of Britons currently bank by telephone.
The research will come as welcome news to the nation's banks, which are pouring millions of pounds into developing telephone banking, and at the same time closing branches and slashing staff numbers. According to Bifu, the banking union, 120,000 jobs have been lost in bank branches in the last six years and thousands more are expected to go.
Competition is already fierce, and will get more intense. Four building societies are due to convert to bank status this year, and all four of them will use phone banking to compete with the existing high street banks.
The supermarket chains are also getting in on the act. Sainsbury's recently announced a phone-based banking service in partnership with Bank of Scotland.
Telephone banking was pioneered in Britain by First Direct, which was launched by Midland Bank in 1989. First Direct is still expanding and will announce shortly that is opening its first call centre outside Leeds.
The experience of First Direct shows it can take years to make any money out of phone banking because of the high investment needed in technology.
First Direct did not make any profits for Midland until December 1995 and since then has wavered back and forth between the red and black depending on the resources being ploughed into advertising.
First Direct dealt with 10 million telephone calls last year and aims to field 12.5 million by the end of this year. On average, a spokesman said, First Direct recruits 12,000 customers a month and has over 600,000 in total.
The example set by First Direct jolted other banks into offering telephone banking. But most of these services differ to First Direct as they are run in addition to traditional branch banking rather than as an alternative.
For instance, NatWest, which caused uproar from unions by announcing plans to cut 10,000 jobs in branches in the next four to five years, has around 540,000 customers using its telephone banking services.
Kartik Natarajan, analyst at Datamonitor, which based its research on interviews with 200 banks across Europe, expects Britain to have Europe's highest penetration of telephone banking customers in 2001 at 32 per cent or 13 million customers.
"Competitive pressures across European retail banking markets will force banks to set up telephone banking operations in order to meet customer demands, although in some countries banks will have to work hard in order to persuade their customers to transfer to such services," he said.
Britain was currently behind only Finland and Sweden in its penetration of telephone banking and would grow to the highest proportion because of changing work patterns in Britain, the efforts of the banks and sophistication of the telephone network, Mr Natarajan said.
Lloyds TSB, which estimates that 560,000 of its customers are banking via the telephone, is already preparing for the next era in banking with plans next month to start a television banking trial at 250 homes in Hull.