Boris Johnson has been filmed at a private garden party telling Conservative members that the NHS absolutely needs to be reformed, as he fired them up for a general election by asking them to be ready to “wallop Jeremy Corbyn”.

The frontrunner to be Conservative leader and prime minister was videoed giving a rabble-rousing stump speech to members in Sutton Coldfield on Saturday, the day after the Guardian revealed that police had been called to his girlfriend’s flat following a late-night altercation.

Asked by one party member what he would do with the NHS, Johnson told the crowd the health service was a “crowning glory” but was “not getting the kind of support and indeed the kind of changes and management that it needs”, suggesting he as prime minister would aim to undertake an overhaul of the health service.

He said Simon Stevens, the NHS chief executive, had once helped him get elected president of the Oxford Union as a student, and together they would “sort things out”.

In remarks that may alarm those opposed to another reorganisation of the NHS, Johnson said: “It needs more money but where you are absolutely right is that it needs reform.”

His delivery in private appeared to be more energised than at a separate public appearance at a hustings in Birmingham on Saturday, where he refused to answer questions from the moderator Iain Dale about the row with his partner, Carrie Symonds. He told Dale the audience did not want to hear about “that sort of thing”.

At the garden party, Johnson got cheers and cries of “you’re the man for the job” as he told members that his plan was to “get Brexit done, relaunch our party as the party of modern progressive conservatism and then get ready to wallop Jeremy Corbyn”. Asking for their support, he also promised to “knock Jeremy Corbyn into a cocked hat where he belongs” in an apparent sign his sights are fixed on an election.

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On policy, he mostly concentrated his 10-minute stump speech – likely to be repeated to party members across the country – on the need to improve policing, faster broadband and wealth creation.

His biggest applause from members was for his attack on Corbyn for being a “Hamas-supporting, antisemitism-condoning, Hugo-Chávez-admiring apologist for the Kremlin”, whom he branded “deranged” for wanting to embark on a programme of renationalisation.

The day after the furore over the row, Johnson went to private events in Bicester and Sutton Coldfield as well as the Birmingham hustings.

The next day, his whereabouts are unknown but a photograph of mysterious provenance appeared on Monday appearing to show him sitting with Symonds in a Sussex garden on Sunday. Johnson declined 26 times to say how the picture emerged, when it was taken or why it was released to the Mail Online.