Paula Sherriff, a Labour MP, said: "Frankly, the Secretary of State should have been here today".
She also held several meetings with representatives of charities and NGOs involved in aid and humanitarian work.
The global development secretary, Priti Patel, held undisclosed meetings in Israel without telling the Foreign Office while accompanied by an influential pro-Israeli Conservative lobbyist, it has been reported.
Ms Patel apologised on Monday for 12 unauthorised meetings with senior Tel Aviv officials in August - including Mr Netanyahu, his Public Security minister, and chief diplomat - behind Mrs May's back.
"Patel didn't think it was worth telling Theresa May that she had met with a foreign leader on Friday morning - more than two months after she had returned to the United Kingdom", stated PoliticsHome editor Kevin Schofield.
A government spokesman said Ms. While away I had the opportunity to meet a number of people and organisations. "There is no United Kingdom financial support for the Israeli army", a Downing Street spokesperson said after it emerged that in the wake of her visit in August, Patel had discussed potentially providing some of Britain's aid money to Israel's armed forces which run field hospitals in the Golan Heights area.
"I can see how my enthusiasm to engage in this way could be mis-read, and how meetings were set up and reported", Patel said in a statement. The Foreign Office, it said, was "clear that United Kingdom interests were not damaged or affected by the meetings on this visit".
"I am sorry for this and I apologise for it", Ms. Patel said in a statement.
Patel said she met with senior Israeli figures, including Prime Minister Benjamin Netanyahu, the Foreign Ministry' Director General Yuval Rotem and opposition leader Yair Lapid.
They also discussed the Israeli domestic political scene, India, Netanyahu's then-forthcoming visit to London to mark the centenary last week of the Balfour declaration, and "prospects for closer collaboration between Israel and the United Kingdom on development and humanitarian issues". The Telegraph also reported that Patel had suggested to Netanyahu that the United Kingdom should give aid to the Israeli army.
"This is another out-of-control minister in [British Prime Minister] Theresa May's weak government, but this time with implications for Britain's standing in the world as an honest broker and model for fairness in distributing aid".
Prime Minister Theresa May has directed the UK Cabinet Office to look at how the country's ministerial code of conduct can be tightened in the wake of one of her minister's meetings in Israel not being disclosed through the usual channels. May yesterday summoned Patel to No 10 to "remind her of the obligations which exist under the ministerial code".
Downing Street said the premier had accepted her apology and considered the matter closed.