In the past few weeks Israel has been in the headlines for all the wrong reasons. There have been punch-ups with the outgoing Obama administration, which, consistent with decades-old policy on settlements, chose to abstain from a landmark UN vote rather than exercise its veto to block it. There were reportedly threats of war to nations that voted for the resolution. A case of an Israeli soldier who was sentenced for shooting a severely wounded Palestinian attacker saw what Israeli newspapers describe as “hooligans” descend to intimidate judges and the army. While the mob spat and shouted, Israeli politicians sought to inflame rather than cool tempers. Finally in Britain this week the Israeli ambassador had to apologise to foreign office minister Sir Alan Duncan after an embassy official was caught on camera in an undercover sting plotting to “take down” MPs – including Sir Alan – regarded as outspoken supporters of a Palestinian state.

There is no more serious a charge for a foreign embassy than its staff meddling in British government affairs. A British minister writing anonymously, to protect himself from abuse and character assassination, in the Mail on Sunday claimed that Britain’s politicians had submitted to lobbying, “taken donors’ money, and allowed Israeli influence-peddling to shape policy and even determine the fate of ministers”. Only the week before Theresa May scolded US secretary of state John Kerry for calling out the current government in Israel for what it is: “the most rightwing in Israel history, with an agenda driven by the most extreme elements”. It was either a bone-headed intervention by the prime minister – given that Britain helped broker the UN vote – or a craven attempt to ingratiate herself after being snubbed by the Israeli government. Neither looks good for Mrs May. An investigation into influence-peddling into this most sensitive of foreign policy areas is needed to get a sense of whether parliament or government is being corrupted. The foreign office has declared the matter closed, but it should not end there. Crispin Blunt, chair of the foreign affairs select committee, was elected with a remit to look at the lobbying by both Palestinians and Israelis and the effect on British policy in the Middle East. The terms of his committee’s inquiry should be wide enough to look at whether pernicious influence was wielded by either side.

What has changed is that while Barack Obama stuck to the script of US foreign policy in the region, his successor, Donald Trump, says he won’t. Mr Trump has nominated as ambassador to Israel David Friedman, a donor to the settlement movement, who is if anything to the right of Israel’s prime minister, Benjamin Netanyahu. The family of Mr Trump’s son-in-law and Middle East adviser Jared Kushner has donated to illegal settlements. This will suit Mr Netanyahu. He heads a coalition of rightwing radicals accused of seeing democracy as being synonymous with unchecked majority rule. This political messaging has changed Israeli society: in a poll last year four-fifths said Jews in Israel should be given preferential treatment. Half thought Arabs should be expelled.

This accelerating rightward trend leads to a situation where the occupation in the West Bank becomes seen as permanent, and further annexations envisaged. Israel would find it difficult to be a Jewish and democratic state if Palestinians did not have their own nation. Foreign ministers meeting this weekend to discuss the peace process should remind Mr Netanyahu of where he is heading. Mr Trump’s endorsement of Jerusalem as Israel’s capital by moving the US embassy there – a US congressional law not implemented by previous presidents – would be a disaster for peace. Mr Netanyahu, in the spotlight for graft allegations, portrays himself as a strongman. But he has been a weak prime minister who rules through acquiring multiple offices of state. Meanwhile the rhetoric of reaction goes unchecked, which is a road to ruin.

• This article was amended on 12 January 2017. An earlier version referred to Tel Aviv where the Israeli government was meant.