Guys and Galls,
I'm no expert however, I have visited Heysham many times. Not for the nettle beer either.
Be careful that's the watch word. Both the power station and the harbour have been under "scrutiny" for a long time. Issues ranging from terrorism during the troubles in Ireland, gun running to illegal immigration and importing are sensitive subjects.
There is a similar sensitivty in parts of airports, where there are no go areas with cameras. Terrorism being the main reason.
Anti terrorism laws are far reaching.
As long as you are on a public footpath and not causing obstruction you should be OK. However security gaurds have their own interpretation of things.
You could approach the harbour authority to get clarification of what and where you can photograph and any restrictions on equipment. You may get mixed inerpretation from the police.
They don't have the right to confiscate equipment, memory cards, film etc. But you could be guilty of trespass, if you don't have permission for your activities or are in restricted or private areas. Anti terrorism laws have more power including arrest, and questioning in the polkice station.
If in doubt retire to the Strawberry Gardens, if its still called that, and reflect through some amber nectar.
Cheers
Ned