If ICI's bold plan to split goes ahead, Barnes, rather than the group's better-known chief operating officer, Ronnie Hampel, will head up the glitzy pharmaceutical part, ICI Bio.
With him he will take 70 per cent of the group's profits and a third of its turnover. Bio's value will dwarf that of its sibling, the rump industrial chemicals business.
Sir Denys Henderson will remain chairman of both companies, but the clear impression - which Barnes does nothing to dispel - is that he will run his own show.
If to the outside world this seems a very considerable plum for a man previously little known, it is less of a surprise within the imposing walls of ICI's Thameside HQ.
There the 56-year-old Barnes has long been noted as a strategist. At 34, he was the youngest director of its powerful pharmaceuticals arm. Later he was credited with the quiet but radical transformation of the paints division.
'Ronnie Hampel had been very hands-on at paints,' says an insider. 'When David arrived he seemed very different: he was quiet and sat behind his desk thinking. But it was he who produced the strategy which made the company a world leader. He built the company up, made acquisitions, drove it forward.'
'I do think I have an entrepreneurial flair and an instinctive view of how a deal can be done,' says Barnes. Written, it appears conceited; spoken, it sounds much more like a frank observation. He is by all reports a man who neither minces his words nor is given to speaking off the cuff.
He is equally frank about the way he has chaffed at ICI's notoriously bureaucratic bit: 'It can be frustrating.' But: 'If you have a good idea and are a good advocate, you can get what you want.' This is quintessential Barnes by all accounts - a man who both fits in and gets his way.
The trace elements of his personality are detectable in his background. This is the son of a Nyasaland Provincial Commissioner (Companion, Order of St Michael and St George) who was sent to boarding school (Shrewsbury) at the early age of six. It was an upbringing destined to create a backbone of the upper middle classes, courteous, meticulous and hard working, though not fanatically so.
But in among the traditional colouring lurks an unconventional streak. This is a self- confessed failed vet and a Liverpool University drop-out. 'I suppose I didn't apply myself enough.'
Instead, he took a job as a lab assistant with ICI's then nascent pharmaceutical research centre in Cheshire for a year, before departing for Malaya on national service.
That proved formative. He saw action as a second lieutenant in the Royal Artillery (Command N Battery, Eagle Troop, 2nd Regiment, as his Who's Who entry proudly records). And (presumably) what he learned came in handy on his return to ICI.
'We were 200 miles north of the Regimental HQ. If a phone call came through, you could always say you couldn't hear the instructions.'
At ICI he is liked rather than merely respected, though he can seem distant - a typical Englishman. As he himself explains it: 'I don't apologise for being very English.'
Further evidence for which is his very British obsession with watercolours, and a social conscience.
He was instrumental in raising money to build a hospice in Thames Valley and is occasionally found lending a hand at another hospice with which his wife is involved. He even does his bit for better City governance by acting as a non-executive director of Thorn-EMI.
His children - a daughter Alison who is an interior designer, and a son Jonathan who is apprenticed to a furniture maker - sometimes ask him, with the classic incomprehension of the 1960s generation, why he bothers.
'I say it's because I want to be of service. Someone has asked for my help and I may have something to give.' Something else which looks more pompous than it sounds.