It is monopoly in that it would be very expensive to set up a competitor. It has very high barriers to entry. Sure a company can cherry pick deals to get started but to provide a universal postal service would cost far more than the ability of any company to set up. Why are almost every postal services state owned? Because of the cost.

I can see this going two ways:

A small group of large companies will buy up Royal Mail and work relatively well together and push each others prices down.

Or, many small companies buy up parts of Roay Mail - The "Mid-Wales Postal Company" (let's say) will do all mail for mid-Wales. This could mean that anything I send to my parents in Wiltshire could be extortionate as the MWPC would either have to arrange a van to specially go to Wiltshire, or get the letter so far and pass it to another company who would probably charge for the transaction as well as delivering it as far as they could where it might be passed to another company again...

What happens to the Post Office? My landline and internet are with them and I'd rather not have the hassle of being shunted over to someone else...

If I move will the local post office offer the same services that I currently get here? Or will the company who runs that office choose different services, or fewer services, or the same services with different names or different conditions?

I think that if privatisation was feasible, we'd see the likes of UPS/CityLink/TNT/etc. doing domestic mail a bit more now.

The post office is safe for now. Though if the private companies were to offer domestic mail deliveries they would want higher rates and it will be run into the ground.

I imagine it will be similar to mobile phone companies. Sending mail to Wales will be like calling cross-network, with "termination charges" being passed back to the sender. Alternatively, it could be like the US model where the termination charge is paid by the receiver, but I can't see Brits swallowing that...