While fixing the extractor hood yesterday, I accidently hit a wire when drilling and exposed the copper. The wires are too tight to get some kind of a box in there and putting an electrical tape may be too fiddley.

Any advice will be greatly appreciated even if you believe hiring a tradesman is a better option.

See the pictures attached:

After repaired by the pro:

A DIY repair may be possible, though ugly, even if the wires are trapped so you cannot pull through any extra length or a replacement length of cable. Attach a 1-gang box to the wall in exactly the right place so you can cut the cable and bend the ends upwards into that box from below on opposite sides. Join Live to Live, Neutral to Neutral and Earth to Earth using screw connectors and short pieces of wire to bridge the gap. The bridging wire must be the same gauge as the cable ... easiest source is a bit of offcut cable, probably 2.5mm, and the screw connectors must be rated for 30A if that's a ring main. Put an informative label inside the lid to help anybody wondering what the heck it is, and screw the lid on. You now have an accessible junction box as required by the rules, that looks like an old socket box that's been blanked off.

THe lesson for the future is to invest in a buried cable detector device, and to always use it before drilling holes in walls. These detectors aren't expensive., compared to calling out an electrician....

Obviously, safety considerations like isolating that circuit are paramount, and note that even if that circuit's breaker is off, then the neutral touching earth can still trip the Earth Leakage Circuit Breaker...

Find the socket / box that that wire goes to, disconnect it, then pull it out from the other end (which you need to find - either in the roof space or under the upstairs floor) then replace it.

If the copper has been damaged then just covering over with tape may not be safe.

Looking at the plastic cover, this looks like you are in the UK. You can hope that the wire is not totally trapped somewhere...

Given the size and location of the wire, It looks like you hit the range feed which may draw upto 50 amps. Such high current applications require greater care in making connections such as splices. in general there are two safe approaches to repairing this damage. The easiest but most expensive (since you have conduit and assuming that it is continuous) is to pull the wire out, repair the conduit and pull new wire. A cheaper variation if local code allows hidden splices is to cut the damaged location in the wire and crimp slice (with a good crimper, probably hydraulic given the wire size). The other option is to put in a splice box with a splice rated for the current.

I do not recommend just repairing the insulation as you have damaged the copper and ranges are a high current appliance.

By the way you are quite fortunate not to have started a fire as if you had hit both wires . . .

Insulated crimped connections are allowed in the UK, and considered maintenance-free so they can be concealed. A proper ratchet crimper is essential. The whole should then be wrapped in self-amalgamating tape.