if you own the house, look up a qualified local electrician on one of the Comptent Person sites such as NICEIC.
I would want to run it under the floor; but electricians are not good carpetlayers and not especially good at carpentry (though better than plumbers). Rubber-backed carpet will probably flop back OK, a good woven one ought to be re-stretched.
If the floor is chipboard (probable) the electrician may be able to poke the cable between the joists using a flexible rod. If he can't do that, he can saw the boards and lever them up, but if they are nailed-down chipboard they will probably squeak afterwards. A nicer job is to have a carpenter in but this will put the price up. Eccentric people like me have floors of ply, screwed down so you can easily take sections up for this purpose.
I would not recommend going to all that trouble unless you were having additional sockets all round the room, or the floor was coming up anyway because it had cracked or you were having plumbing work done. If you have the floor up for a socket, you might as well have several sockets, TV points, LAN cables and speaker systems done at the same time. Have plenty.
For a cheap, slightly inferior job, you can run the cable round the room stapled to the top of the skirting. Don't ever run it under carpet.