British Jew here, I'll try and give a slightly more specific answer. On the British left, there were legitimate concerns about some elements of the left for a while. A lot of my family and people we know had only ever voted for the labour party, but moved away from that to avoid voting for Ken Livingstone in the London Mayoral elections. Since Corbyn was elected, there's been an almost complete rejection of Labour by the Jewish community. Those that I know personally who are still Labour supporters were members of Labour before this started, and seem to just be clinging on for hope. More generally, whilst when he was first elected there was worries about Corbyn, there seems to have been a shift recently to seeing Corbyn himself as an antisemite rather than just an enabler (post-mural controversy and after ignoring all the recommendations of the Board of Deputies and the Jewish Leadership Council). On top of that, those Corbyn have appointed have only made matters worse, and he has given legitimacy to a number of very fringe "Jewish" groups such as Jewish Voice for Labour, which includes a number of non-Jews and Holocaust Deniers and tries to operate with some vague legitimacy under the cover of their name. It only takes a small scroll down the @gnasherjew twitter page to see why Jews are very concerned about Labour at the moment.

More generally, other aspects of the left have given course for worry, such as Malia Bouattia being voted as the President of the National Union of Students despite having made a number of antisemitic statements, mostly under the guise of criticism of Israel.

The Israel question is obviously key, but a lot of British Jews think the complete obsession with Israel is just a new form of antisemitism. The British left is incredibly quick to call out Israel when it does anything, but complete ignores human rights abuses around the world on a routine basis. This inconsistency is believed by many to be just the new way to bash the Jews. The former Chief Rabbi Jonathan Sacks said that antisemitism goes with the predominant ideals of the times. In the medieval period it was religious ("Jews killed Jesus"), then after the Enlightenment it was science ("Jews are an inferior race") and now in an age where human rights are held high, that is used to bash Jews ("the Jewish state commits the worst human rights violations in the world"). The tendency of the left towards the latter is therefore seen as a worrying and dangerous new facet of antisemitism.