Patel apologized for failing to comply with the usual procedures that oblige ministers to inform the British Foreign Office before doing official business overseas and said she regretted her statement that Foreign Minister Boris Johnson was aware of the visit in advance.
The meeting with Lapid became public knowledge after the Yesh Atid leader tweeted a photo of it.
He said: "She also had meetings with a number of charities and I find it utterly unsurprising that the worldwide aid secretary would want to talk to charities while she's on holiday in a particular area about whether or not we can use the British aid budget to diminish the humanitarian problems there".
Labour accused International Development Secretary Priti Patel of committing four "serious breaches" of the ministerial code over her trip to the Middle East in August. Details of her meeting with senior Israeli politicians including the Israeli Prime Minister Benjamin Netanyahu were revealed by the BBC last week.
"Patel has a history of showing favouritism to Israel and is suspected to cut or divert the essential aid that the United Kingdom sends to the Palestine Authority", Slaughter told MEE.
Embarrassed by the revelations of the 12 meetings she held in 12 days during a "family holiday" in Israel, Patel attempted to diffuse the incident insisting last week during comments to the Guardian that the British Foreign Secretary "Boris [Johnson] knew about the visit".
The Foreign Office said it rejected the call, because it involved humanitarian operations in the Golan Heights, illegally occupied since 1967. The secretary of state would like to take this opportunity to clarify that this was not the case.
Senior Conservatives believe Patel should be "toast", says The Daily Telegraph. Today's statement acknowledges that the quote "may have given the impression that [Patel] had informed the Foreign Secretary about the visit in advance".
"She saw the Israeli prime minister with a donor lobbyist, and failed to declare or admit to the meetings".
Such meetings could constitute a violation of Britain's ministerial protocol.
When asked whether the PM had been made aware of anything else that was discussed that could constitute a change of policy, Number 10 replied: "What I am clear on is she set out the people she met and from looking at the list of people it is quite clear the different areas they cover".
Downing Street officials are already furious with Ms Patel, who has also admitted misleading journalists about the Israel trip. In any ordinary circumstances a member of government embarking on a secret diplomatic mission and holding unauthorised talks with a foreign power would be an instant firing offence.