So far most of the nuclear power discussion has been about grid electricity.
Even if the UK replaced all its nukes it would only offset a small proportion of current CO2 emissions (something like 5%) because other major energy consuming sectors use other sources of power than the grid eg gas home heating, industrial use of gas, coal and oil, aviation fuel for aircraft, petrol and diesel for cars and lorries.
The proponents of nuclear will actually achieve little or nothing in terms of emissions reductions (if they get their way) if overall energy consumption continues to rise - nukes will just provide the power taken up by the increased consumption.
What we really need is across the board demand reduction through a massive programme of efficiency improvements, new technologies and a switch to low carbon grid generation if we are to cut UK emissions substantially.
Nuclear is a red herring in this debate - and retains the serious drawbacks of risk, waste and its own form of non-renewable fuel – uranium. ‘Peak uranium’ looms in about a hundred years time at present consumption rates.