I'm not too sure what people ( on here and in government ) mean when they talk about Regional Connections.
With more capacity at Heathrow, Regional then means not just the UK, but includes all of Europe.
There are hundreds of MAN, BHX, EDI equivalents all around Europe from where passengers are required to fly to a hub for an onward connection - and this is why AF, KL, LH offer all those flights to UK and European.Regional airports to capture those passengers. Quite often, point to point traffic for, say, EDI > CDG is less than 10% of total passengers on the flight.
With more capacity and slots, expect BA to be able to challenge AF, KL and LH on much more equal terms, which would be a huge gamechanger for IAG and especially BA and more non-UK Regional Airports will see LHR as a viable Connecting Hub instead of just CDG, AMS and FRA / MUC as it is at the moment.
On the other hand, I've no idea whether IAG include the value of their LHR slots on their Balance Sheet - but if they do then they would have to write these down and which could be £billions with currenly impossible-to-get, scarce LHR slots reportedly changing hands for $50 million a throw.