By all accounts the heli did not declare an emergency, so considering he heliport is perhaps a 1/4 mile away? The controller would have seen both visually and by looking at the metar that the weather was not suitable.
As has been posted by others the view from the VCR at Battersea is less than ideal in certain directions and you do not be come visual with traffic landing on 21 until they are quite close, you certainly cannot see traffic at Vauxhall.
With regards to the weather; if it is below the prescribed minima the heliport is closed.It's that simple. There are plenty of visibility points and a cloudbase recorder to assist he ATCO in doing the met obs.