Just a short line from another Transpondian [UK here]
In the UK most older houses are brick & plaster. Only newer [& cheaper] constructions use what the US would call 'drywall', any decent modern build would use concrete 'cinder-block' & plaster so this is a very common situation.
Mounting on any trim, such as skirting, panelling or architrave is not allowed, so you have to surface-mount [unpopular] or chase the wall.
The standard method is to chase down into the brick & plaster - either old-style with a hammer & chisel, using a channel-cutter as mentioned by PhilippNagel, or more commonly using an SDS drill set to hammer only & using a large chisel/spade bit.
You can drop from the ceiling or come up from the floor, whichever is most convenient.
Later edit: I'm not certain whether to traverse horizontally is against code, but it is certainly frowned upon. People expect cabling above or below a socket & plan their picture hanging etc activities accordingly. They don't expect a wire horizontally. Using a cable finder is, of course, always recommended.
Once the drop is in, you then re-plaster.
Conduit is not required in the UK for such construction [though it is optional], only that metal back-boxes are embedded [plug & screwed] in the wall to carry the sockets & terminals. Any jointing must also be metal boxed. Back-boxes come in two common depths [25mm & 35mm; 47mm is less common, 35mm is 'standard'], depending on how much room you have to work with in the wall, single- or double-wall brick & whether you need sockets in-line on both sides of the wall.
UK Trade store link as example, presumably wouldn't fit US sockets so for illustration only.