I've been on the receiving end of quite large plants, sent through the post, by nurseries, and delivered by the postman. Some nurseries do a great job of packing plants, complete with pot in some cases. They often use a plastic bag tied round the pot and secured with a rubber band, to keep the compost in place.
David Austin sends out his bare-rooted roses using the ordinary postman. They are sent in large tough plastic bags, which are very damp inside.
If sending any compost beware that it's heavy. You ought to weigh it at home, to see how much postage is likely to cost before delivering to a post office. There's a thingy on the Royal Mail website which tells you the cost of a packet, if you know the weight in grams...
I was in Homebase yesterday and noticed that they have a service where customers can send parcels anywhere wordwide, by packing whatever they want to send in a yellow DHL cardboard box (provided). No idea of the price.
Sending someone a plant is a nice thought, but the cost of postage might be several times the cost of a new plant.