Ofcourse, Blairite MPs will like nothing more than Corbyn gone.
The real issue is - there is a lot of anti-Semitism the world over (US/EU/ME). But by accusing anyone and everyone who is opposed to the current Israeli government policies as an anti-Semite, they have weaponized the word for their own political objectives rather than actually try to reduce the problem. Even as Jewish reporters I know continue to get floods of real hate mail daily. Just in the US - while everyone was bullying Omar to apologize for saying AIPAC pays money to get political influence (Republican leader threatened Omar and another Muslim rep on twitter !) - a dozen Republican senators/representatives sent obvious anti-Semitic messages (about Soros) - or because of what Trump said, an unhinged white supremacist gunned down people at a Synagogue.
Lets be clear here - within the Jewish community there is a clear divide on what is and what is not anti-Semitism. Hardliners want to call out anything progressives say about Israel as anti-Semitism, where as liberals do not.