It's tricky to have Britain doing a lot of investment in nuclear power for a couple of reasons. First, by the 1980s you start having a fairly significant anti-nuclear lobby, which means that you really must have started major investment earlier than that so that there will be enough momentum to overcome those issues. Second, prior to about 1970 or so, oil and coal are too cheap and too easily available for major investment to start. Together, that means that you have a 10-year window, with earlier dates being much preferred, for a big nuclear build-out to start. Unfortunately for the OP, Britain--in contrast to France--also has large native oil and coal reserves, and relied (I believe) much more heavily on coal than oil for electricity (France got about 39% of its electricity from oil). That meant that they were less affected by the '70s price shock than France. Further, the '70s is about when all that native oil and gas was being discovered and started being produced. All that makes it very difficult for Britain to start a major nuclear program.
Perhaps if you have several major disasters in the early North Sea exploration, so that BP, Shell, et. al. become soured on them and turn instead towards Nigeria, South America, etc. for more oil/gas, the British government sees nuclear power as a good way to reduce dependence on unreliable foreign producers of oil (uranium is mainly produced by Canada and Australia--together they amount for a little more than 50% of modern production) and to supplant falling coal reserves. But that's kind of a stretch. Perhaps more useful would be avoding Three Mile Island and Chernobyl, so that anti-nuclear protestors have to work off of more theoretical arguments than they could IOTL. That might make them weak enough that the Brits might start investment in the '80s, although the Thatcher government doesn't strike me as being particularly friendly to the kind of governmental backing that would be needed for that.