There is no solution to the problem of nuclear waste.

Despite over 50 years of nuclear power in the world there is still no safe storage solution for the enormous amount of nuclear waste that has already been produced. Britain has not even begun detailed planning of a waste store, which will take decades to construct. Large volumes of highly radioactive – and lethally toxic waste will remain a danger for hundreds of thousands of years – many times longer than the whole of human history. Having even more new nuclear power stations will mean leaving an even greater legacy of this poisonous waste for future generations to deal with$1  
with. 
 
Trying to predict a realistic cost for nuclear waste storage is extremely difficult. Plans in the UK for an underground site are still just on paper – no location has yet been found. There is no knowing if an underground store would retain its structural integrity over the extremely long timescale that is needed – hundreds of thousands of years – especially when you take into account any future geological events like earthquakes$1 
earthquakes. 

There is a massive distrust of nuclear power, that is for sure, but whether such distrust is viable is another issue. The fact is that the three historic nuclear disasters (1957 Windscale Fire, 1979 Three Mile Island and 1986 Chernobyl) killed fewer people than the oil and coal industries have. So why is the risk of harm used to argue against nuclear power? 
 
In addition to the comparatively low risk, modern reactors are safer now than the ones built 20/30 years ago, which means the risk is lowered still. This line of argument is not a government spin; it is common sense that technology is continually improving, especially in the energy sector.