Most long distance mail is routed via air nowadays - much quicker than trains!
Royal Mail operate a hub at East Midlands Airport, with (if I remember correctly) flights to and from Bournemouth, Exeter, Stansted, Edinburgh and Belfast - which pretty much covers it (if you conveniently ignore Wales and the more remote areas of Scotland, which can be connected by Road or other means relatively easily). Some used to be operated by Titan Airways, not sure if they still are. Road travel from those hubs to most localities is likely to be quicker than any train could manage, and more reliable given the commonality of late night engineering works.
Of course, British Airways aircraft all carry the Royal Mail logo too
Given all the other postal firms are run off the back of existing logistics organisations, I'm fairly certain that there's no regular agreement for any postal service by rail unless it's a small/local/ad-hoc affair.
EDIT: Looks like my memory needs updating - they seem to have a much more comprehensive operation now:
East Midlands Airport said:
The Royal Mail domestic air network at EMA consists of 11 outward flights to the more distant UK airports serving the remoter areas of the country. Boeing 737 aircraft operate 8 of the flights with smaller aircraft used on flights to the Isle of Man and Aberdeen in the North of Scotland. This network is vital to ensure first class mail is delivered next day throughout the UK.
These 11 aircraft also bring mail in for transfer to 75 major mail centres. Around 50 tonnes of mail is received for inward transfer each night. That is about 1.1 million letters and packets.