Hmm, tricky and probably not likely (more due to his "Marmite" reputation/personality than his politics) but certainly not impossible. Idea for how he gets to power first off:
In Place of Strife passes in 1968. This reduces strike action overall and introduces partial employee ownership into the British economic mainstream. In annoys the more radical wing of the TUC overall, lowering their opinion even further of the Labour leadership. It also ends the closed shop, which decreases union membership and would hit the many (many) smaller unions harder, encouraging mergers. Many politicians and union bosses favoured mergers as larger unions theoretically weakened the power of the stewards to agitate for strike action. Its been argued Britain's trade union woes of the 1970s weren't that bad in terms of total work hours lost compared to contemporaries but the sheer number of strikes by smaller unions that really made the difference both economically and in the minds of the public. However as big unions like the NUM show, that doesn't automatically equal moderate labour relations.
Fewer strikes doesn't mean the 1970s is great for Britain though. You'll still see economic chaos to some degree. Have Heath win in 1970 and survive 1974/5. Its a hung parliament but Heath and Thorpe come to an agreement. Many in Labour are convinced it will collapse quickly so Wilson holds onto the Party leadership by his fingnertips for most of the decade, becoming increasingly stale. He is basically forced out.
In the meantime the Lib-Con government make no effort to hold a referendum on the EEC, as Labour did in 1975 IOTL. Although anti-Brussels feeling was nowhere the level it would get to (1975 ended in a 68-32 split to Remain) it was not inconsequential and the lack of a referendum would have effects. The Labour membership was anti-EEC 2 to 1 in the mid-70s. Labour backbenchers were often split down the middle on EEC related legislation put forward during the 1974 Wilson government. Similar to how Thatcher would lead Tory MPs to support Wilson's EEC legislation to ensure it passed, you could easily see similar from the Labour Right to the Heath government of TTL as the Eurosceptic wing of the Tories rebel.
Heath was great at negotiating and schmoozing one-on-one but pretty tone deaf to public relations. I can see him managing to woo the Liberals for a few years to stay in power while pissing off the Tory Right and making public gaffes as was his style. You also have Jenkins & Co angling for the Labour leadership (let's say Callaghan's health leads him to retire early), while claiming the 1974 general election result was proof the public was pro-EEC and there was no need for a referendum. Chuck in some anti-EEC news stories (Cod Wars etc.) and a growing public opinion that is less anti-Brussels than pro-referendum, the likes of Benn claiming the EEC has not been an economic magic wand and the lack of a public debate shows its the whim of the Establishment.
Benn was IOTL and even more so ITTL the face of Euroscepticism (Powell was close but outside the relative mainstream). It is on this issue he beats Jenkins to Labour Leader, not simply anti-Europe but played as a populist pro-democratic movement. It is also a slap to the Labour Right as a whole, who many feel have let the side down ever since In Place of Strife. Ironically many opponents of these reforms back Benn, who is pretty keen on worker ownership.
Benn as leader would be far from flawless and might have a fair few gaffes. A Gang of Four style split is likely but it might happen differently. Here Labour has not just been kicked out of government but is seemingly just waiting for the Lib-Con government to collapse. The careerist types would be less inclined to jump (I'm looking at you Owen), while fearing a Labour government would equal leaving the EEC, maybe Jenkins, with less support for a new party, simply crosses to the Liberals as he had considered.
If Jenkins and a few people cross over to the coalition benches, it can be jumped on as a symbol of the patricians of all three parties uniting to defend the free-market swindle known as the EEC. Tribal loyalty is very strong in the Labour Party, even to this day. By joining the Liberals, the ideas and allies of Jenkins still in the Party would be worth bugger all in the short term - poisoned by 'treason'. You may also see some traditional conservative MPs leaving, becoming "Democratic Labour" and the like.
Now the Heath government finally enters it last act circa 1977-1980. Sunningdale has been a worse mess than OTL thanks to Heath just not giving up, meaning more violence, maybe even Unionist paramilitaries attacking more Government targets, claiming London is trying to betray them. 'Quit Ireland' is slowly becoming a thing. The labour reforms have limited strike actions compared to OTL but a big confrontation (say the Miners' Strike is simply put off for a few years) finally brings the whole edifice crumbling down.
Hell on top of the EEC, union tensions and Northern Ireland, let's throw in some nukes. During the Heath government's last days a very scary cock-up happens involving a US nuke. A scare, no mushroom clouds over Norfolk but enough to shit people up and lead to pointed questions in Parliament about how much oversight the government has over foriegn WMDs on British soil.
An election is called, lets say summer of 1978. You have a tired government led by an unpopular PM, the right-wing of his party very unhappy, the moderates stained with the economic malaise and grubby compromises of coalition government. Labour election posters show the three heads of Heath, Thorpe and Jenkins, representing the stale status quo.
Benn, formerly Labour's election guru, is aware of the need for a good campaign and maybe even bites his lip and hires some big marketing folk to help out. The message is simple and populist - the consensus politicians are undemocratic and out of touch, unwilling to take bold action in the face of Britain's many problems, which naturally they helped cause. It might be a little too cute to have an iconic "The Conservatives Aren't Working" poster but you get the idea.
The message is rather than socialist, democratic, focusing on "putting power in your hands". Benn promises a referendum on the EEC and a full national debate, which leads Enoch Powell to once more openly back Labour as the only chance of ending the European experiment. Peter Shore, a fellow Eurosceptic Labour Left figure with a patriotics streak, is central to the more 'nationalistic' part of the campaign, attempting to woo over Tory and floating voters to what is ultimately a pretty radical Labour Party in the name of the country.
The effects of In Place of Strife creating a more moderate, concentrated elite of TUC bosses, combined with watching Heath 'prune' the national industries has led Benn to decide the 1945 ideal of state industries and strong unions means squat for the socialist revolution when the TUC bosses are dining with Heath, and a nationalised industry can be easily privatised once more. So his 'democratic' policy extends to economics, give workers larger stakes in the economy, to entrench 'their' ownership over that of unionists or government officials. Note this doesn't mean Labour's campaign would anti-union but it would focus on the foot soldiers over the bosses. This also makes it much harder for future governments to privatise if the employees have a direct financial stake. This is combined with devolution of power (including devolved assemblies), establishing national referenda as a common means to decide major issues. All of this gels pretty well with Benn's OTL views.
Benn wins an okay majority that is stronger than Labour's popular vote. The Tories and Liberals are stained by the chaos of the 1970s and keen to blame each other, while the various *SDP exiles lack organisation and due to Jenkins' tarnished reputation are wary of an electoral alliance. Due to the optics of the election as change versus consensus means these candidates' impact of splitting the Labour vote is limited, with non-partisan Eurosceptic voters voting Labour outweighing defectors.
That was a lot longer than I expected! I might write some ideas about the Benn government itself later.