Yes and no.
There are 2 beams on Astra 2E. A UK spot beam and a pan-european beam. The UK spot beam is much tighter over the UK than any other existing beam from any of the Astra satellites.  C5, 5USA etc. moved onto the UK spot beam on Astra 2F last december, we then lost them on 1.2M dishes.

Astra 2E is theoretically identical to Astra 2F and will have the same footprints.

The BBC announced in december that they would be moving to Astra 2E:
http://www.bbc.co.uk/blogs/blogaboutthebbc/posts/Changes-to-BBC-Satellite-transponders-in-2013

Astra 1N is due to be moved and so it's channels will be moved onto another satellite, almost definitely 2E, this is where all the BBC and ITV channels are.

2E is in orbit, is being tested and, from the signal levels I've seen, is comparable with 2F so hopefully we will get sufficient signal from it but with a larger dish.

So, those are the facts. The rest is speculation but makes sense.

The BBC and ITV have no reason to broadcast to Europe - they get no financial benefit as noone pays a TV licence and advertising is targeted at UK residents so they will move their services to the UK spot beam to attempt to restrict access to their programming from outside the UK.

SKY shouldn't broadcast to Europe but do. SKY receive financial benefit from subscribers so are well aware they would lose millions in revenue if they moved to the UK spot beam so any channels they move will almost certainly move to the pan-european beam.

One other point to clarify - SKY do NOT broadcast the BBC or ITV programmes - they come from a different provider - Freesat.  Just because the BBC etc. channels are on a SKY digibox does not mean you will continue to receive them after the moves. BBC and ITV channels are NOT part of the SKY subscription package.