The Big Six not only all supply a proportion of nuclear electricity, they have all shown an interest in building new nuclear power stations.
It is economic circumstances, rather than any opposition to nuclear, which has seen five of the six back away from nuclear new build in the short term.
EdF is at the vanguard of new nuclear. The state-owned French utility, along with its new Chinese partners, is planning to build a new nuclear power station at Hinkley; intended as the first of a new tranche of nuclear power stations in the UK.
Hinkley still hangs in the balance, but that it is even a possibility is due to the enormous subsidies and financial support extracted from the UK Government, plus the financial benefits for EdF and its Chinese partners in being predominantly state-owned.
Centrica, British Gas‘s parent company, were involved with EdF till February 2013. Centrica cited increasing costs and a lengthening construction time for its decision to drop out of new nuclear. 
German utilities E.on and RWE were planning 4 to 6 new nuclear reactors in the UK till selling their stakes in the Horizon Nuclear Power joint venture to Hitachi in 2012. 
The move followed the German Government’s move away from nuclear power in the wake of Japan’s Fukushima disaster. But any link would seem to be the financial consequences of the investment changes required in their home country rather than any anti-nuclear stance by the utilities.
RWE’s website still states (as at 15-4-14): “Building new nuclear power stations is a key part of RWE npower’s commitment to meet the UK’s energy needs and to reduce carbon dioxide intensity.” 
SSE and Scottish Power were planning new nuclear in a joint venture, NuGen.
SSE was involved in the NuGen consortium, till a reassessment of its investment options led it to sell its stake in 2011. It did not rule out a return to nuclear investment in the future. 
ScottishPower’s parent company, Iberdrola, sold its 50% share in NuGen to Toshiba in 2013 for €102m  due to financial pressures which has necessitated a continued selling off of assets following €850m raised in 2012, mainly from disposal of wind farms. 
For the latest developments in the UK nuclear industry, visit No2NuclearPower.org.uk.
 BBC News, 4 February 2013 http://www.bbc.co.uk/news/business-21319031
 BBC News, 30 October 2012 http://www.bbc.co.uk/news/business-20134735
 RWE website (accessed 15 April 2014) https://www.rwe.com/web/cms/en/393616/rwe-npower/about-us/our-businesses/our-approach/
 Press & Journal, 24 September 2011 http://www.pressandjournal.co.uk/Article.aspx/2450101
 Reuters, 23 December 2013 http://uk.reuters.com/article/2013/12/23/uk-britain-nuclear-iberdrola-idUKBRE9BM04N20131223
 The Telegraph, 14 January 2013 http://www.telegraph.co.uk/finance/newsbysector/utilities/9801070/Iberdrola-shelves-Scottish-Power-stake-sale.html