Yes, you will be able to receive local programmes and in Northern Ireland, Wales and Scotland some broadcasters also provide extra services as well.
Regional variations are as follows:
ITV1 - You will receive the local variation depending on the geographical location of your transmitter.
Namely one of the following- Anglia, Border, Central, STV in Scotland, Wales, West, London, Meridian, Tyne Tees, UTV in Northern Ireland and Westcountry.
ITV2 & 3 have no regional variations
BBC One - has regional variations in Scotland, Wales & Northern Ireland. These appear exactly as they do for analogue viewers. (Local news broadcasts correspond with geographical location of the transmitter station)
There are also Scottish & Northern Irish digital variations of BBC Two which can differ slightly from the local analogue versions.
BBC Two Wales is only available as an analogue signal and a channel called 2W is broadcast in its place for Welsh digital viewers. 2W shows more local programming than BBC Two Wales but their schedules are usually very similar.
BBC Three, BBC Four & BBC News - have no regional variations.
Five - have no regional variations.
Channel 4 - is the same in England, Wales, Scotland & Northern Ireland.
Welsh viewers can only get the UK version with digital TV. Analogue viewers get S4C instead which has a high content of Welsh language programming.
Digital viewers get the UK Channel 4 and S4C (S4C digital is part-time 1100-0000) too.
Digital viewers also get S4C2 which is a part-time daytime service broadcasting coverage of the Welsh assembly.
Bid TV & QVC - are both only broadcasting part time in Wales.