the most basic check would be to turn off the power, remove the socket faceplate, and look for loose, missing or unconnected wires.
In a ring circuit (typical in the UK) there will be a cable coming into the socket from each side; each will have a red, a black,and an earth wire. The two earth wires should be sheathed in green & Yellow (you can buy this in most hardware stores) and should be connected to the earth terminal of the socket, and there should preferably also be a short, G&Y sheathed, link to the metal back-box earth terminal.
The fault might be in the socket that indicates faulty, but it can also be on one or both of the sockets next to it on the ring. To have a fault indicated on a Ring socket there are usually at least two wiring defects
so check all sockets for bad connections.
If the wiring you find is not as I describe, please say what you find. If you can post a picture of the inside of the socket that will be helpful.
We would also like to see a pic of the fusebox/consumer unit, the meter, the suppliers fuseand the area and wiresaround them, to see what sort of installation you have.
edit
I see Spark123 and bernardgreen have already mentioned most of this. But please do the inspection and let us know what you find. Otherwise ask around friends and neighbours for a recommended electrician.