My fusebox doesn't have a lock on it, and a quick look at Screwfix Online doesn't seem to indicate new boxes have one, so I'm guessing it's not needed.
As to the rest - too many unanswered questions to be more specific. Is this a completely new fusebox and socket (no previous wiring), or is it an addition to an existing, aleady wired, property? If the latter, do you need to take a fresh cable out of the fusebox, or can you extend off an existing circuit somewhere? Is the existing wiring sound - reasonably new, or ancient? Is the existing wiring done on a "ring main" system?
The easiest way to add a socket to an existing setup is to extend off that existing setup. If it's modern, it's likely to be a ring. The easiest point to access an existing installation is at an existing socket. In its simplest form, you would
- design the route for the cable from where you want the new socket to be back to the closest or easiest existing socket (note: NOT lighting installation).
- position the new socket and route the cable. Use the right type of cable. 2.5mm2 minimum. If it's concealed in a channel then I believe it has to have a protective cover over it, before you plaster over it. You may prefer to use mini-trunking on the surface if the cosmetics don't bother you.
- connect the cable to the new socket following the coloured wiring convention.
- turn off the power and ensure it stays off
- open the closest or most convenient existing socket
- bring the new cable into the back of the socket. You may need to break a hole in the back box. You should always use a rubber grommet around the hole.
- (This is the hard part): connect the cable ends into the back of the existing socket ensuring the existing cables don't disconnect as you do so. Note that, if it's a ring there will be two sets of cables already attached to that socket. Again, match the coloured wiring convention.
- reassemble the old socket, turn on the power and test.
You can't add more than one outlet to any one single point on a ring by a simple extension. If you (ever) want more then you should extend the ring itself, which is somewhat more fraught.
Have you considered simply using an extension cable, plugged in to an existing socket, clipped or concealed under floorcovering, if you prefer?