The only nuclear ships in the UK are a few submarines. I doubt they couldn't operate in the warmest ocean temps, but maybe they couldn't operate at peak performance. One noticeable difference in the British nuclear subs is they use a scoop injected condensate system for heat transfer. I'm sure they also have pumps or it wouldn't work at the dock, but the point is to shut the pumps off when moving fast enough to be quiet. So they can operate in warm waters, they just may not be as quiet.
I sort of doubt this is actually the case though because all you need is enough cooling to condense steam in a separate loop. The turbine almost pull enough energy out to condense it there and it become "wet" instead of "dry" steam. Now you just want to pull a little more energy out to make it liquid so it can be pumped. It's all under pressure so we aren't talking boiling at 100 C but this is happening more like 400 C. The system is designed to be efficient and need as little cooling as possible on the steam side just enough to change the state from steam to almost boiling water.
Here is a PDF about some different land based cooling. I learned on a reactor in the desert where all the cooling was done on a closed loop and then through evaporator towers. It make the whole system a little less efficient, but they is so much clean energy available in Nuclear power a little wasted energy for more safety and less impact in a remote desert seems like a good idea.
https://www.google.com/url?sa=t&sour...nunt0bCz-WGTLJ