The simple answer is that *some* overlap is allowed. The EU rules seem to allow it, and BDUK allows it.
However, the real answer is much, much, more complicated.
First, the EU rules specify that subsidies cannot be used to supply an "area" that already has service (ie grey or black areas). But they don't specify that subsidy cannot be used to supply a "white area" when such supply also happens to overspill into supplied areas. This makes for a hole in the rules.
So ... some LA's have interpreted the EU rule very strictly, so don't allow overlap. Others have been more flexible.
Second, the rules just talk about "area" when discussing overlap. In some places, "area" gets deliberately treated as a postcode area - especially when mapping. In other places, it is more suitable to talk about the cabinet coverage area. Such confusion between "area" makes it easier for "strict" LA's to be even more immovable.
Third, central BDUK have (seemingly more recently) specified that "white areas" need to include a substantial majority of VM coverage before they would be turned into a "grey area". It seems that this "significant majority" is being interpreted as 90% - so BT would not be allowed to cover "an area" (with subsidies) if 90% of it has VM service.
Fourth, once the LA's have encapsulated the individual "area" within the definition of the total intervention area, they have proven to have little flexibility to alter it ... at least in phase 1. Some areas have realised this problem, and are making the definition more malleable for the phase 2 SEP.
That means that LA's that want to be more flexible probably can't be until phase 2 - so long as they have gone through a new OMR.
It also means that strict LA's have to be first persuaded that they can be more lax, and then persuaded to include these new rules in their phase 2 OMRs.
I wrote a whole lot more over over in this thread
, but it is a little wordy and confusing.