Who really represents British Jews?

It's certainly not who Corbyn thinks - that's a tiny minority. But Britain's 'official Jews' of the BoD, JLC and CST also only represent a tiny minority (namely the Left leaning and lukewarm supporters of Israel).

Note that the BoD officially takes the UK Government failed "Two State Solution" view on Israel and believes the whole of Judea and Samaria ('the West Bank') - and even East Jerusalem - must be part of a future Jew-free State of Palestine. Also note that, whereas the BoD/JLC includes (and some would say is increasingly dominated by) Yachad - an extreme leftist anti-Zionist group, they actually work against any groups or people who are strongly pro-Israel Zionist (by which I simply mean realists who believe that handing land to the Palestinians will not work). That is why the BoD/JLC do not represent the vast majority of British Jews - who tend to be centre/right and realists on Israel.

Update: I just responded on Facebook to a claim about the elected deputies in the BoD being representative with:

Irrespective of the deputies, the BoD is the organisation which lobbies to ban strongly pro-Israel speakers (Geller, Spencer, Im Turzu etc), works with Islamist groups to censor strong pro-Israel voices (Hopkins, Robinson etc), while at the same time being happy to engage with multiple Islamist antisemites. With the exception of the (very weak) Arkush the leadership is dominated by people whose idea of being 'pro-Israel' is to deligitimize Israel's democratically elected leaders. The BoD has NEVER represented the overwhelming majority of British Jews who support Israel unconditionally. And recent events have proven that the BoD is a complete waste of time since it has failed to prevent the mainstreaming of antisemitism.

Previously (and yes this is directed at BoD/JLC, CST etc):

And if the BoD really wanted to do something to stop the tsunami of antisemitism they would be devoting their efforts to exposing the lies and indoctrination of Palestinians - much of it funded by UK taxpayers - that drives modern antisemitism (disguised as anti-Zionism), along with the cult of 'Palestinianism' whose lies about the Jewish state are fed to those only too happy to believe so that they can promote their hidden antisemitism under the respectable guise of anti-Zionism.