Depends how you look at it.
It IS a viable solution to our energy WANTS... but the problem is - how does one dispose of the waste?
At the moment we seem to be burying it in other countries. This is ok, until there is a particularly poorly placed earthquake, that tears a hole in the shielding and irradiates a massive patch of earth. This is inevitable, as the amount of waste from Nuclear stations will go up as we use more, and the half life of this stuff is millions of years... so its not going to rot away like our landfill will in a few generations... oh no, this stuff is here to stay. So thats a particularly scaremongering argument, but look at it a bit more sensibly and it just doesn't really make sense:
The energy we get from the sun is free, so's the energy from the moon (via the tides), wind and all the other sustainable energy solutions are freely available and dont suffer the waste problem.
IF as much money was spent on researching these technologies as is spent on nuclear research/maintenance/disposal/clearup then we would be well ahead...
Unfortunantely a lot of people have vested interest in nuclear technologies for, say, blowing up other countries who don't conform to our views. So there we are.
It is A solution to our problems, but its short sighted (like a lot of the 'solutions' in our civilisation) and will ultimately be destructive to someone, somewhere.
NB: I'm not claiming that sustainable power sources don't have their destructive problems too - a recent report shows wind turbines are killing bats.. but this is where we need research to protect against such problems, and that will only come if there is a big enough pressure for it from people instead of accepting the nuclear option and not worrying about the problems for future generations!)
Another point here is that we need a LOT of sustainable power generators to meet our energy fix - nuclear fills that gap nicely, but the real key is that we should be trying to use less power too.

The short and sweet answer is no.

Aside from the issue of waste and the impact of a major accident (the more nuclear plants there are, the more likely a major accident will occur - plus the plants may be come targets for acts of terrorism), these issues go against nuclear:
a) the fuel for nuclear reactors will peak just as oil etc. has/will and there are doubts about the continued availability of uranium;
b) the UK would have to rely on other countries for the fuel;
c) lead time for planning, construction and commissioning can be very long (and we do not have the time);
d) water consumption is high per unit of output which is a potentially serious in a world of uncertain weather; and
e) nuclear would almost certainly divert investment from renewables.