My experience has been that the brass body of the hose bib is almost always sound and that to try to remove it can lead to much more work than you are prepared for. I think most plumbing or hardware stores will stock all the replacement parts you will need, including a kit to "dress" or smooth out the sealing surface where the washer closes against. Also, seriously, look for an old guy like me in your neighborhood who has all the parts you'd need, to rebuild several spigots, and would be glad to share.
Those are such a common type of faucet that you may want to just consider replacing the whole thing. They should just screw onto a pipe that extends out beyond the brick work by about a 2 to 3cm.
Only issue you may have to deal with is that it would be a good idea to grasp the pipe on the inside of the wall so that it does not turn when removing the faucet. A buddy or partner on the other side with a pipe wrench should do the trick.