Either the prime minister or the BBC has no clue about what nuclear power is for. 93% (pdf) of the UK’s oil consumption is for uses other than electricity generation (e.g. transport) so it makes no sense to argue that nuclear power is a solution to the current oil crisis. (Put another way, oil accounts for 1% (pdf) of the UK’s electricity generation). If you want to solve the power cuts, well that’s a different question (though nuclear isn’t necessarily the right answer to that one either).