The decision to go non-nuclear was made around 1993-94. Back then we were all scratching our heads as to what to do with the western reactors that were approaching end of life, not to mention the Russian ones.
Surface ship reactor disposals were seen at the time as particularly problematic. We didn't have then (and still don't have now) anywhere to put the reactor compartments in the long-term once removed from the ship, as evidenced by the 7 boats still at Rosyth and the 10 or 11 in Devonport. The US nuclear recycling programme has a large trench on the Hanford reservation where they can store the RCs long-term.
United States naval reactors - Wikipedia, the free encyclopedia
Their Nuclear Ship Recycling Programme has been a real success, but has cost a lot of money.
All of that is before you include the design challenges of putting a reactor in a surface ship. The risk appetite for that was simply not there in the mid-90s and given where we are now, it was the right decision, although ironically the industrial base in terms of skilled people would probably be better off and there would be a little less risk in the PWR3 programme.