No need to do that straight away. Find the horn under the bonnet and
check the wires to it. The connector may have corroded or simply fallen
off. If anything else has stopped working at the same time then check the
fuses as well.
If you know anyone else with a mini then try connecting your horn up to
their car and see if it works in that. If it does then you'd just be
wasting money replacing it.

Basically the fault is either:
a) horn
b) wires
c) fuse
d) switch stalk

To test the last one, find a local scrap yard with some minis lying
around and try to find a stalk. Just unplug the connector from yours and
connect the other one in and see if it starts working. If it does then
buy the second hand stalk from the scrap yard, if not then chuck it back
(you'll have to agree with the owner on that though).

Christ, if I had electrical components burning out I'd want to know what
was up and have it fixed presto so that nothing else burns out. Sounds
like you need to replace the stalk and check all of the wiring/fuses to
the stalk to make sure there's no shorts..