Their rhetoric is not a liberal rhetoric. The Left campaigned for the UK to stay in the EU. The Right campaigned for the UK to leave.
Only in a Bizzaro World does a "Real Leftist" support the far-right's rhetoric and policies and oppose the rhetoric and policies of the Left. In that Bizzaro World, Trump (who supported Brexit) is the true Leftist and Bernie (who opposed it) is really a right wing apologist for bankers and multinationals.