Which do you really mean by "Having a power cut"? Is it:
1) You have had a power cut (Whole street or a number of houses without power)
2) The supply just to your own house has failed?
3) The supply just to your sockets has failed?
4) The supply just to the cooker has failed?
My guess is that it is probably 3 or 4, in which case one would suspect the element has failed in the part of the oven you were using at the time or maybe very possibly wither a wire has been trapped, especially if the element has been changed before or very possibly a cable has been damaged between cooker and wall.
There are plenty of videos and advice already out there about how to check and, if necessary, change oven elements. It just needs a Google search to find.
Acp, September 2017