Thanks for all your comments. I've spoken to the (very helpful) electoral department at the local council.
Each council should have a list of polling stations used at the last EU election. However, polling places may not be available on the day of the next General Election. Councils are usually notified a couple of months in advance for they can check if a particular place is available.
You can only vote at your designated polling place - this is usually your nearest. There may be some exceptions.
There should be no trouble getting a list of polling stations. However, it may be too time consuming and expensive to provide a list of every post-code in the area matched with the polling station.
So, it looks mostly doable. I think I'll ask the Electoral Commission for the email address of each returning officer - then I'll ask them for what details they have. I may go down the FoI route if they're not forthcoming with the info.