Boris Johnson’s newly appointed Conservative party chair Oliver Dowden hopes to model himself on one of his most high-profile predecessors, Cecil Parkinson, Margaret Thatcher’s right-hand man, as he readies the party for the next general election, his allies say.

Dowden’s allies said he wanted to “beef up” the job of chairing the party, making it a more public-facing role as well as preparing Conservative Campaign Headquarters (CCHQ) for an election campaign.

Parkinson, a champion of Thatcherism from a working-class background, frequently appeared on TV to explain Tory policies. He ran the 1983 campaign that led to a landslide majority, before stepping down later that year as it emerged at the party’s conference that he had fathered a child with a former colleague.

Dowden represents Parkinson’s former seat of Hertsmere, and aides say he is keen to replicate his predecessor’s election-winning ways – if not his complicated private life.

Wednesday’s reshuffle was conducted with a firm eye on the next election, which is due in 2024 but could come earlier. Dowden told CCHQ staff on Wednesday that they should start getting into campaign mode now. “You can’t fatten a pig on market day,” he said. “It’s time to go to our offices and prepare for the next election.”

Trusted by No 10, he is tipped for a return to a senior cabinet role if he succeeds in reshaping CCHQ.

His predecessor, Amanda Milling, relentlessly toured Tory-held seats in the “red wall” and beyond, her Twitter feed peppered with pictures of herself alongside MPs in their constituencies, but there were doubts in Downing Street about whether she had a grip on the party’s campaign machinery.

Many Conservative MPs blamed what they saw as complacency in CCHQ for the loss of the Chesham and Amersham byelection this year to the Liberal Democrats, and the failure to take Batley and Spen from Labour.

Some party donors also privately raised concerns about what they saw as a lack of direction under Milling. One said: “The donors are basically running CCHQ now.”

No 10 may be hoping that “Olive”, as Dowden is known by colleagues, can rein in his co-chair, Ben Elliot, the flamboyant party fundraiser who has generated a string of negative headlines in recent months.

One senior Tory who worked in CCHQ during the last three elections contrasted 2015 – when David Cameron had given the consultant Lynton Crosby more than two years to hone the party’s strategy – with 2017 and 2019’s snap elections with hastily assembled campaigns.

“Cameron brought in Lynton and gave him two years to get the operation into shape and prepare for the 2015 election. Boris is doing the same with Olive and getting him to properly sharpen the operation in good time,” they said.

In 2019 Johnson’s campaign focused on the simple “Get Brexit Done” message. Crosby, who is known to remain in touch with the prime minister, has said Johnson needs to focus on convincing voters who backed the Tories in 2019, perhaps for the first time, that he has acted on their concerns.

Crosby said these voters “will be looking to see if the investment they made with their vote is delivering the return they wanted in terms of the attention to their issues and an understanding in response to the problems that they felt they faced”.

That is likely to mean pressing ahead with the government’s “levelling up” agenda, though some Tories are also concerned about the party’s vulnerability in “blue wall” seats in the south of England, many of which the Liberal Democrats are targeting aggressively.

As culture secretary until Wednesday’s cabinet reshuffle, Dowden was a key foot soldier in the government’s “war on woke”, wading into rows about the removal of historic statues and picking fights with the National Trust. He cut his political teeth as an adviser to Cameron, and a former colleague described him as “ultra-political and razor-sharp”.