Sir Lynton, nicknamed the ‘Wizard of Oz’ for his skill at crafting election campaigns, was knighted in 2016 as a thank you for masterminding David Cameron’s big 2015 win. He has said that the most important factor in a campaign is a message that connects emotionally with voters.

But he has also been criticised for pushing monotonous, focus group-tested slogans, and for dabbling in ‘dog-whistle’ politics.

Crosby was part of the inner circle of Tory campaign strategists in 2017 and was caught up in the post-election blame game, though an official party review found he wasn’t at fault for the result.

CTF submitted the second and third biggest single invoices of the election according to the Commission: £882,000 ($1.6 million) on April 28 and the same amount again on May 18.

Both amounts were invoiced for “opinion research” for the Conservatives.

A note attached to the second invoice noted it was a “consultancy invoice … obviously separate to any of the research services which are invoiced separately”.

CTF also billed £480,000 ($867,000) for “strategic advice and consulting” on April 19 and again on May 18, and £288,000 ($520,000) on April 28 and again on May 18 for “opinion research”.

CTF has increased its fees: invoices to the Tories in 2015 totalled £2.4 million ($4.34 million).

But the biggest invoice of the 2017 campaign was not connected to Crosby: it came in early June, just a week before the election invoicing over £1.2 million ($2.17 million) for Facebook and Instagram advertising by the Conservatives in the month before the election.

The Tories spent more than three times as much as Labour on Facebook and Instagram advertising.

Overall the Conservatives were invoiced £2.1 million ($3.8 million) by Facebook, compared with £577,000 ($1.05 million) to Labour and £412,000 ($744,000) to the Liberal Democrats.

The Conservatives were by far the biggest spenders overall, too: they spent £18.6 million ($33.6 million), compared with £11 million ($19.8 million) by Labour and £6.8m ($12.3m) by the Liberal Democrats. All campaigning parties and groups spent a total £41.6 million ($75 million), compared with £39 million ($70 million) in 2015.

The Conservatives also paid £544,000 ($983,000) to the Messina Group; Jim Messina, the strategist behind Barack Obama’s 2012 re-election campaign, brought expertise on how to target ‘persuadable’ voters on social media.

May’s chief advisor Nick Timothy, who resigned after the election, blamed “campaign consultants” for the Conservatives’ poor performance.

In a column written after the vote, he complained the campaign had not used ministers effectively and had not reflected “the insight that took Theresa to Downing Street in the first place”.

However an internal Conservative Party review found the fault lay with a disastrous election manifesto, the lack of a supreme campaign chief and a dearth of local campaigners.

Both the Conservatives and Labour are under investigation by the Electoral Commission for submitting spending returns that were missing invoices and for submitting potentially inaccurate statements, the Commission said.

Fairfax contacted Sir Lynton for comment but had received no reply at time of publication.