Not an LHR controller myself but have worked at LHR for nearly 5 years. One of the benefits is supposedly an increase in the flow rate, hence more slots available for airlines to use.
One of the major problems Heathrow has is with the lack of stands so if you increase the slots available then you need more stands. Terminal 5 will create more stands but then T2 will be closed while Heathrow East is developed so there might not be too much of an increase.
There are a lot of other issues associated with this which I have seen discussed on here before but I will let an LHR Controller answer that one as I am merely an Airline Ops controller!!!