I don't think the BBC was biased towards a remain vote, as always I thought it was very balanced.
Andrew Neil really went for Osborne and others, there was lots of pro leave stuff on their too.
The problem with the BBC is actually that because it is neutral, if you hear it giving one side of the argument you will go "oh its biased" but when you see it give yours it doesn't register as much. Essentially you are looking for it to be biased and so find confirmation in that fact when it reports something against your POV.
There was some academic research done into it, and it turns out that the BBC gives slightly MORE coverage to pro right wing, pro business, anti EU stories than the other way around. It was done by Cardiff Uni and confirmed by another.
The thing to ask yourself is why would the BBC destroy its reputation for impartiality by doing this?
Certainly not vested interests because it gets funding, the money the BBC gets from the EU works out as about 0.06% of its budget.