LONDON — Britain’s embattled prime minister, Theresa May, got a break of sorts Tuesday from the sprawling sex and sleaze scandal that has already forced the resignation of a cabinet minister — but only because her weakened government was embroiled in two new crises.

On vacation in Israel, the international development secretary, Priti Patel, held 12 secret meetings, one with Prime Minister Benjamin Netanyahu, and discussed sending aid money to the Israeli authorities. Back at home, the foreign secretary, Boris Johnson, made an incorrect statement that could mean more prison time for a Briton imprisoned in Iran.

In normal times, either scandal might prompt their resignations, as opposition politicians have demanded.

But these are not normal times in Britain, which is negotiating its fast-looming exit from the European Union, or Brexit, a bitterly divisive issue that often appears to have paralyzed the government.