Antony Jenkins, the former chief executive of Barclays, has spoken of his surprise at being sacked by the bank's board, saying he believed he needed between five and 10 years to overhaul the culture of the bank.

In his first interview since he was fired in the summer after just three years, Mr Jenkins said the bank was performing well when he departed.

"It is a source of regret to me that I wasn't able to complete the work," he told me.

"But when I look at what we achieved in three years I'm confident that the organisation [is] in much better shape. I'm proud of what I achieved, but I'm also very proud of what the people of Barclays achieved in working with me over that time period."

I asked him if he was shocked when he was told by John MacFarlane, the chairman, that the board wanted him to leave.

"Well, I'm a human being, so I have to say that it was surprising to me, but I completely respect the authority of the board in choosing the CEO," he said in the interview for Radio 4's In Business programme.

"And I'm realistic. I've been in corporate life for over 30 years. These things happen.

"The bank was performing very well.

"After 3 years of incredibly hard work, we had real momentum and you could see that in the results: statutory profits were up 25%; our capital position had improved immeasurably; we'd actually achieved our 2016 targets 18 months earlier; costs were under control; the culture was changing and reputation was improving; we'd built a leadership position in technology and that was paying dividends for us."

At the time he departed, Mr MacFarlane thanked Mr Jenkins' for his work but said that a new style was needed for the next stage of the bank's development.

Some investors had raised concerns that the bank was not profitable enough, particularly on the investment side of the business.

The new Barclays chief executive, Jes Staley, formerly of the US investment bank, JP Morgan, started work this week.

Mr Jenkins said that the overall culture in banking had changed since the financial crisis but there was still a long way to go, particularly on issues of high pay.

"In certain areas of banking there are people who bring in a lot of revenue for the company and it's arguably fair that they should be compensated for what they do," he said.

"But I also think if you look at any area of life where you've got people who make a lot of money, it's always hard to justify compared to what the average person makes."

He said at least the days when people were paid handsomely "just for showing up" were over.

Mr Jenkins also said he understood that many members of the public felt that the banking sector had not been sufficiently punished for the chaos of 2007 to 2009.

"I think that's a very understandable reaction," he said.

"It's a reaction which is shared by people who work in the industry as well as by people in society at large.

"If you look at how close the world came to a very, very perilous situation in 2008/9 and you look at the cause of that and you look at the institutions that failed and the institutions that had to be supported by taxpayers around the world, you would have to ask yourself where is the accountability, where is the culpability there?

"A lot of work has been done, as you know, to put in place mechanisms that will allow if such a thing happens again - and we hope that it doesn't - for individual accountability to be there, and I think it has to be there frankly."

Mr Jenkins is chairman of Business in the Community, the organisation that promotes responsible behaviour by firms.

The issues of trust in business are, of course, not just concerned with banking or the financial services sector.

The latest scandal involving VW and emissions testing shows how bad practice can infect any firm.

"Trust has never been lower in business," Mr Jenkins said.

"Part of that is to do with transparency and there's a lot more transparency today than there was 30 or 40 years ago and that's a good thing.

"But when Business in the Community was established over 30 years ago, at its heart was this notion that businesses should act responsibly.

"And that means that we're in business to make a profit, of course we are, but we make a profit by serving our customers, by fulfilling our obligations to society and by providing great work environments for our colleagues.

"I always got frustrated with people in the industry who said: 'Oh you know it's just a PR problem. They don't understand how much tax we pay, how many people we employ, the great things we do for the economy. If we only told our message better then they'd all love us.'

"I don't believe that for a minute. I think this is a product much more of what you do than what you say and so it's really in businesses' own hands to demonstrate to society that they make a positive contribution.

"I think there's a new generation of leaders in financial services who have much greater appreciation for these sorts of issues and you just have to look at the share prices of banks before the crisis and after the crisis to see the massive value destruction that happens when you don't run the business in the right way.

"It is empirical - there's no way to avoid that data."

Banking 'Uber era'

Mr Jenkins says banking is facing a technological revolution which could be as destructive in employment terms for the traditional banks as the financial crisis itself.

He describes it as banking's Uber moment after the app that allows customers to call a minicab from their smartphone - and almost single-handedly revolutionised the taxi business in cities around the world.

Mr Jenkins argues technology companies (known as FinTech in the jargon) will be far more efficient and better for customers in providing financial services and what are known as "back office" operations - all the filings and book-keeping that at present keep a small army of people in work.

For the more than one million people directly employed in financial services across the UK, there is a cold wind coming.

"If you look at the traditional banking sector, it's already under immense pressure because of weaker macroeconomic environments and regulatory change," Mr Jenkins said.

"At the same time there is the threat from the FinTech startups, which to date has been relatively minor but will increase over time.

"My view is that most incumbents will struggle to transform themselves fast enough to be able to compete with the start-ups and risk getting pushed back down the value chain into being essentially a capital intensive utility.

"The challenges that the banks face is going to result in a rather significant reduction in the number of people employed in the traditional financial services sector and, for example, the number of branches, and I estimate that there will be somewhere between a 20% and 50% reduction over the next 10 years."

The spectacular upheavals of the financial crisis might be coming to an end - another huge change, according to Mr Jenkins, is about to hit.

In Business is on BBC Radio 4 on Thursday 3 December at 20:30 GMT or you can download the programme podcast.