Sir Brian Pitman, chief executive of Lloyds TSB, told a group of business leaders that companies could benefit from "much lower costs" by contracting out many of their activities.
"I don't think we have fully confronted the opportunities in outsourcing and what the consequences will mean for our business as we really grab the opportunities of much lower costs ... by getting business done elsewhere," he said.
Addressing a conference to launch "Leading People", a study of leadership in financial and business service sector, Sir Brian said that increasing competition would lead senior management to consider "much more outsourcing than we have at the moment".
In a reference to the whole of British industry, he said: "It is not a question of producing quality products at a high price, it is producing top quality products at the lowest price possible."
Companies in widely different sectors such as British Airways and North West Water are already taking advantage of the low salaries earned by proficient and English-speaking Indians. Data-processing staff in the sub-continent generally earn around a tenth of the salaries received by British colleagues and so the burgeoning software industry in India can comfortably undercut in-house services in Britain.
A report by the Delhi-based National Association of Software and Service Companies pointed out that the sub-continent had "the second-largest English- speaking scientific and trainable manpower pool in the world".
While it started from a low base, the association calculated that the Indian software sector had grown 46 per cent annually between 1990 and 1995 - almost twice as fast as the business in the United States.
The author of the leadership report, Amin Rajan of the research consultancy Create, believes the resurgent interest in "outsourcing" could mean banks farming out cheque processing, insurance companies contracting out the payment of claims and securities dealers outsourcing settlements. Tens of thousands of jobs are involved in such activities. One chief executive of a banking group told Mr Rajan that 15 per cent of the company's costs could be saved by contracting out money transmission.
In the 1980s companies began by outsourcing in-house services such as catering and cleaning, then proceeded to farm out information technology systems. Next an increasing number of "core" activities will be contracted out, he believes.
However, Mr Rajan argues in the report that the first "outsourcing" wave would benefit companies in the UK.
Countries like India would begin to benefit later as the cost advantages became clearer and knowledge of their expertise spread.
Ed Sweeney, general secretary of the Banking Insurance and Finance Union, expressed concern about the trend. "There is nothing that can't be outsourced if they put their minds to it, but they can sacrifice quality and they can also lose control."
He said that the cost savings could often be illusory. He detected that some companies were already taking back some activities which they had previously "outsourced".