That change could raise a few eyebrows in the City, where the conventional wisdom is that the quietly spoken Randall is little more than an MFI apparatchik, dancing to Hunt's every tune.
But closer inspection suggests that Randall is very much his own man, and his style promises to be considerably different from either the flamboyance of Hunt or the streetwise dealmaking of MFI's founder, Noel Lister.
"For the past few years we have been too focused on survival - understandably," said Randall, "because the recession years were very tough for us. But now we have got to a state where we can go to the next stage. We are accelerating product development, because with the housing market so quiet you need new products to tempt people to buy. And we are beginning to rethink the use of space. John Gummer's restrictions on new developments out of town have changed the game. Such space is no longer cheap and we have to make better use of it."
On the drawing-board is a plan for MFI to take its warehousing out of the stores and concentrate it in cheaper industrial estates, each depot serving a network of satellite stores.
Joint ventures with other retailers are another possibility, and Randall may launch a different retail name to segment the market. MFI tried this in the 1980s with a pilot chain called Ashton Dean, but the project was cut short by the group's ill-fated merger with Asda 10 years ago. So he is testing an idea called HomeWorks with experimental product lines: the most successful go into the main stores.
But Randall recognises that MFI still has an image problem. While he insists that the days of ill-fitting flat-pack furniture are long gone, and the jokes are slowly dying, many people remember MFI the way it was and have not been back since.
"We pissed off a lot of people and we realised in the 1980s that poor quality was costing us money," he admitted, "but I think that people coming into an MFI store today would be surprised at how high the quality is. About 80 per cent of our customers are bringing in repeat business, but the trick is to bring the others back into the fold."
Although Randall's village birthplace is now officially deemed to be in Humberside, like many fellow natives he thinks of himself as a product of Yorkshire's East Riding.
His father was an engineer at the local mental hospital, and he recalls a country childhood full of summer camping by the river. "No one had a car in them days," he pointed out, "so I got the bus 10 miles to school every day. I went to Hull once a year if I was lucky."
But he wanted more than that. Ironically, in view of his success at MFI, when he left school at 16 Randall started selling chipboard for a public company called Hollis Bros, long since taken over by Robert Maxwell.
"One of my schoolteachers knew the managing director," he explained, "and he was a terrific salesman. But if he was angry he would throw things. When I resigned he threw all the contents of his desk at me and then literally threw me out of his office. I learned a lot from him - about selling, at least."
Randall's first job was selling hardwood, but at the age of only 21 his volatile mentor let him start a new venture, importing plywood and chipboard.
When he was 24 he risked his boss's wrath by quitting, because he belatedly realised that he needed qualifications.
"After my selling experience I was attracted to marketing," Randall explained, "but I changed my mind when I found I couldn't do graphs. You had to be able to do that to get a marketing qualification, and I was always getting them the wrong way round. Much to my surprise, however, I was reasonably competent at figures, so I trained as a management accountant. But that's life, isn't it? You can't plan your career, and I just take what comes."
He used his accountancy qualification to get a job with Spillers, the flour and bread business, which was eventually taken over by Dalgety. After six years, Randall became MFI's financial controller - all of 17 years ago.
"But I don't regard accountancy as a be-all and end-all," he added hastily, "not like some accountants do."As with most of his throwaway lines, that remark testifies to years of frustration he has experienced at the hands of the accountancy profession's prima donnas.
He left the Spillers flour, milling and bread group because it was too bureaucratic. "They had 30,000 employees and 100 accountants," he recalled. "That didn't appeal to me: my advice is, never work for a company that employs 100 accountants. I was in the grain and milling divisions and we spent all our time wrangling with the flour and baking divisions about the prices we charged one another. But at the end of the day it didn't matter a damn, because we sold the bread at a loss."
Looking for something more exciting, he answered an advert for MFI. If Randall wanted a contrast, he got his wish.
"The company had a turnover of £30m a year," he said, "and it was a real seat-of-the-pants outfit with a very high staff turnover. It was without a clear structure, and their view was that accountants were to be seen and not heard - preferably not seen either. You learned to get your point across fast, because they didn't give you very long.
"I enjoyed it initially. After Spillers it was refreshing, but it was ultimately unproductive. We were growing so fast that it covered up mistakes. The accounting operations were a shambles."
But for two years in the mid-1980s, Randall could look back on the shambles as a golden age. In 1985 MFI merged with Asda, the supermarket group. It was the sort of scheme merchant banks like to dream up, a merger of two retailers with theoretically offsetting demand cycles. And it was a deal made in hell.
"Those two years were a desperately unhappy time," Randall agreed. "The synergy just wasn't there. They were two very different businesses."
In the nick of time, while there was still a bull market and banks were still willing to lend ridiculous amounts to finance management buyouts, seven directors including Randall bought out MFI for what is still a record £717m.
"Derek Hunt took his chance with the rest of us," said Randall, "and he made me finance director. It came as a shock to him that I knew nothing about MBOs. It was only later that we found that no one else knew about about them either."
But with 39 banks on the white-knuckle ride through a recession severe enough to demand two debt reschedulings, Randall soon got the hang of it.
As soon as there was a glimmer of light at the end of the economic tunnel, in 1992, MFI refloated on the stock market.
At 48, Randall could be running MFI well into the next century - but he is adamant that he will not hang around anything like as long as that.
He said cryptically: "At some stage I will realise that someone else can do this job better than me, and I will then set about finding something else. But I don't think it will be a paid job."