what’s the connection?

I will shortly be heading off back to Hong Kong, and as a result I will be offline for the next few days. As I often do on these occasions, I offer a devious and convoluted puzzle for interested readers to fret over. Actually, I think that this one is easier than A Hard Question, which provides more information about the background of such questions, although it’s difficult for me to make that assessment, given that I devised both puzzles in the first place. So, without further ado, I pose the following question:

What connects the following?
• a London theatre;
• a standard American coin;
• a Roman god;
• a domestic electrical appliance; and
• a police officer.

Of course, you’re not looking for just any London theatre, coin, etc., but if you choose the right ones, the connection should be obvious. You should bear in mind that each of the five ‘answers’ is different (see comment by Rob K. below). If you think you have the answer, you can post it in a comment. If you are correct, I will acknowledge that fact immediately, but I will not post your comment until the end of the month, so that later readers can also try to answer the question.

spoiler alert
The correct solution has been submitted below.