National Westminster has already recognised the dangers, and last week tore up the five-year financial services agreement it arranged last summer with Tesco. However, Tesco easily found another willing partner in the Royal Bank of Scotland. Moreover, Sainsbury this week teamed up with Bank of Scotland to launch Sainsbury's Bank with some of the best interest rates on instant access accounts on the market.
The clamber for savers' money by the supermarkets is only the start of a huge upheaval that Professor Llewellyn believes will result in the banking industry giving birth to the "virtual bank" by the turn of millennium.
"Over the next 10 years we'll see more structural change in the banking industry and more change in the business that banks do ... than we've seen in the last 50 to 60 years put together," he predicted.
Banks, he said, should be concerned and be advised to strike alliances with the supermarket groups - a case of better the devil you know. "These are very powerful pressures on the banking industry. Some banks are going to get into trouble," he warned.
The cause for concern, however, is not that the supermarkets will snatch all the business. "These new guys will never get big market shares but that's not what their damage is going to be. Their damage is taking away the juicy bits," Professor Llewellyn said.
Quite simply, supermarkets will only offer the most profitable financial products. And, because supermarkets are not lumbered with an expensive branch network they have more scope to sacrifice more profit margin than banks do on competing financial products.
This, Professor Llewellyn argued, will give supermarkets and other consumer- orientated companies a significant competitive edge. They will benefit from being sub-contractors to established banks, which have to shoulder a great deal of the associated fixed costs of running financial services.
Supermarkets, he added, may only be the first wave of new entrants into banking. He thinks that British Telecom, which he described as having a branch network in every household in the country, could also pose a real challenge.
Banks are going to need 360-degree vision and will have to overcome the frustration of watching new competitors come and go, dropping out of banking as fast as they entered if only because they discover that making a profit proved to be too much trouble to be worth the effort.
Unlike the banks, which are shackled to fixed costs, from running branches through to the processing of cheques, the supermarkets have only the variable costs traditionally associated with sub-contracting in a host of other industries.
Professor Llewellyn thinks that banks are on a fast track to becoming "virtual", where they would do little more than interface with customers who will be able to get their hands on cash through a multitude of different outlets, and possibly even electronic money downloaded on to cards through the Internet in the not too distance future.
He believes that the banking revolution will also see banks increasingly outsource operations. "I really do believe we're at a defining point in the evolution of the banking industry," he said.
Banks are finally sitting up and taking notice of radical changes that have, and are taking place in other industries. Just as British Airways contracts out its catering services or Jaguar uses a vast array of suppliers to provide the products for its cars, so will banks.
New technology has really been the catalyst of change in banking. A fact best illustrated by the closure of thousands of high street branches since the introduction in the 1970s of automated telling machines. And the ultimate technological development is still only in its infancy. Experts predict that the Internet will be one of the biggest threats to traditional banks.
Banks will still be the core of the industry, but their role will be starkly different. Professor Llewellyn said that banks will become more preoccupied with monitoring the suppliers to which they have outsourced.
But he is aware of a stark anomaly. While cut-throat competition and the need to cut back on costs will drive banks to become virtual or "contract banks", it could also lead to further consolidation in the industry.
He believed the two images can co-exist, with some banks following the big is beautiful route to take advantage of economy of scales, while others take the route of the contract bank.
"There are several small building societies which have a good future because they are going to become virtual," he said. For Professor Llewellyn the importance about these developments is that their "potential" to do damage to the traditional bank.
So, the banks that will succeed will be those prepared to change. Diversification could be one way, the fastest route to which would be to beat the supermarkets at their own game and buy one outright - a kind of "if you can't beat them then join them".