Fleming sat by ING during last weekend's tense negotiations over Baring, and it takes much of the credit - or, if you are in the Wellcome camp, blame - for the Wellcome Trust committing its 40 per cent stake in the pharmaceuticals group to the Glaxo offer.
At the centre of both deals has been an irrepressible Brummie, Bill Harrison. And it is a sign of the changing times in the cultured merchant banking world that Fleming - every bit as blue-blooded as the Baring family - should both realise that it needed to sharpen its investment banking operation and entrust responsibility for the necessary shake-up to Harrison. While he wears the tassled loafers that are still de rigueur in some banking parlours, the loosely knotted tie suggests someone more concerned with getting down to business than becoming a mannequin.
As a fatherless only child brought up in the run-down Ladywood district of Birmingham, he seems an unlikely candidate to run an important chunk of Fleming, still family-controlled and one of the more patrician of the City's merchant banking outfits. At odds with the traditional Eton-Cambridge- Guards image of merchant bankers, Harrison fought his way through grammar school to win a place at the London School of Economics.
His approach to the ING purchase of Barings is revealing. "We had been talking to ING for a reasonable period of time about its ambitions in financial services, with particular regard to merchant banking," he says, "and we had made a number of presentations to it on what it might do. So when Barings appeared on the radar screen, in what were nevertheless unfortunate circumstances, we were able to offer ING our services."
ING sent over a reconnaissance team a day or so after the Bank of England rescue failed on 26 February, met up with the Fleming corporate financiers, and hammered out the deal that was eventually accepted last Sunday.
"We worked quite hard at getting to know ING," Harrison says. "It was relationship-building."
But even someone as outgoing as Harrison cannot expect to be friends with everyone. He is unlikely to figure on the Christmas card list of John Robb, Wellcome's chairman and chief executive.
Losing to Glaxo was bad enough for Robb. But what sent him into barely disguised paroxysms of rage was the way his group was effectively stitched up behind his back in a detailed agreement between Glaxo and the Wellcome Trust. So tightly was that deal laced that Robb had to admit last week that it had put off two potential counter-bidders.
"The Trust felt that what was being suggested [by Wellcome and the would- be bidders] was not possible," Harrison explains. "It could not put itself in a position where it risked potential litigation as well as the possibility of losing Glaxo's bid."
It was another high-profile step along the road to his goal of taking Fleming into the premier league of merchant banks. That was his brief when he was poached from the US-owned Lehman Brothers by John Manser, Fleming's chief executive.
"Our investment banking operations were quite clearly smaller than those of some of our leading competitors," Manser admits, "and I recruited Bill to provide a fresh impetus, to back up success we were already achieving in the capital market area, in raising money for borrowers in Europe and Asia.
"Bill is enormously energetic. It's early days, you may say, but certainly my expectations have been matched by achievements."
Even so, Manser admits there is a long way to go to break into the tightly guarded ranks of advisers to FT-SE 100 companies or their equivalents in Europe and elsewhere. "Most of them already have investment advisers," he says. "So what we have to bring to the party is something over and above the norm. And that really must be the knowledge we have of international markets."
Although Fleming has acted for some big foreign clients, such as Matra and Northern Telecom, according to the latest Hambro Company Guide it has yet to lasso any members of the FT-SE 100 club. So, to knowledge of international markets must be added some extra clout: enter Bill Harrison.
"I get on well with the Fleming culture," he says. "I have built a career that has included some industrial experience. Obviously, the bulk of it has been in the investment banking area, but over that period I have tried to pick situations where I felt there was a willingness to face the sort of change needed for growing the business, which requires a certain amount of boldness and thinking ahead."
On leaving LSE, his first thought was to go into industry, but he was both unimpressed by what he found and inhibited about his own pedigree. "They tended not to be very clear about where your career path would go, and I was actually quite precise - perhaps I had one or two chips on my shoulder at the time," he reflects. "That was when my LSE tutor said: `You're crazy; why don't you think about the City?' I thought, with my accent, they'd feel I'd come to empty the dustbins. I was very reluctant, but he kept pushing me."
So, although offered a job at the Bank of England, he went to the US bank, Manufacturers Hanover, where he received a basic training in balance sheets, risk and credit. "I have to say I really milked that course. I squeezed it like a lemon. Then I came back to London and worked in the Eurobond market and in syndicated loans. I was going round the world financing projects like the Hong Kong underground and the Sao Paolo expressway."
In the midst of all that he did some work in the oil industry, which was enough to bring him to the attention of Alastair Morton, now Sir Alastair and head of Eurotunnel, but then building a team of bright young things to set up the British National Oil Company under the late Lord Kearton.
That lasted for two years until Margaret Thatcher came to power in 1979. She floated BNOC as Britoil, and Harrison went to Lehman Brothers, one of the big Wall Street broking firms, which had helped BNOC to raise money.
"When I joined them I set myself to understand the guts of investment banking and the evolution of the business, where it became less segmented. The Americans were very strong on this aspect, because of their multinational client base."
But Harrison was reluctant to commit himself to working in the US, so he spent a couple of years as finance director of Tricentrol, the oil company, and then three more with Schroders.
In 1986, Lehman approached Harrison again - this time to set up its European investment banking operation. He did that for eight years, but once again the only place left to go was across the Atlantic, which he was reluctant to do while his children were growing up.
So he went to Fleming, where he has been for two years and is still only 46. "Fleming weren't doing a number of things," he says "I think they were not utilising their superb international network as effectively as they could have. And I think the integration of capital markets and corporate finance was not really in place. You actually had two businesses, and the logic in my experience, coming from US investment banking, is that those form part of a single effort with major clients. So the integration of those is important. Then, I think I have instilled a confidence of being in front of larger companies and adding value in the most competitive part of the market place. My team has responsed massively - and the results are beginning to show."
Confidence is something Fleming is unlikely to be short of as long as Harrison is batting for it - treading on a few toes, but otherwise charming his way into the big boardrooms that have so far been closed to the merchant bank.