https://commons.wikimedia.org/wiki/File:Energy_mix_in_France.svg#/media/File:Energy_mix_in_France.svg
https://commons.wikimedia.org/wiki/File:Energy_mix_of_UK.svg#/media/File:Energy_mix_of_UK.svg
France Land Area : About 630,000 km2
England and Wales Land Area (as Scotland will probably not let us build any plants) : About 150,000 km2.
France gets about 30% of its power from 18 plants, so the guess that we would need 32 3.2GW HPCs to fully decarbonise doesn't look too far out (we could probably mitigate this with some renewables with a consequent effect on the baseload capability).
The two countries populations/power requirements are comparable. So we would need to build the same number of plants in 1/4 of the space. Nuclear plants of course have to go where there is significant water supply. In this country that means the coast. I could do a map with 32 red dots on it showing what the UK would look like with this number of plants, but I guess you would get the picture.
Building 32 plants. At the moment it is taking us about 10 years per plant. Even if we could double that to 5 years per plant it is still going to take 150 years to build them all.
These plants create a lot of waste. Yes the high level waste is a relatively small component of that, but the medium and low level waste also needs to be handled very carefully and stored somewhere.
Geological depositories are expensive and risky. See this and the mess that was created :
https://en.wikipedia.org/wiki/Asse_II_mine
The TLDR is that converting to nuclear from fossil fuels is either going to take a long time or be hugely expensive. Probably both. The faster we try to do it, the even more expensive it is going to get.
It's a huge problem if we intend to decarbonise, which is made even worse by the rate at which we are a) not building plants and b) not building enough of any infrastructure to replace fossil fuels, or c) ramping down fossil fuels in a more sustainable way than currently.