Outside socket requires double pole isolation (£6 ish switched fused spur ) indoors, even if spured off a ring final circuit the other side of the wall
Mk Ip66 socket £35 plus cable and sundries
£15 minor works certificate
fuel and cost of van
he'll pay tax obviously
and such a job ,depending on how far away may eat up half a day in time , collecting materials ,getting there and back, testing the circuit ,RCD etc
NIC EIC or approved scheme yearly fee, public liability insurance ,etc etc
so anyone quoting £100 is trimming the cost of all the above somewhere

my daughter had 2 quotes to add 2 double sockets with USBs to her bedroom. One quoted about £150, the other was nearer £200. The cheaper quote gave a start day & time, which was then put back to later in the day which was then put back to a couple of days later. I did them in the end.
yep ,
good electricians are busy people and don't work for peanuts