Well I am afraid that the attire of visitors from the US is one of the things that makes us smile in the UK, although little more than that. Even the men's suits sometimes seem to be made of material we would use for curtains ....!!
However do not worry about needing to bring a suit anywhere, except for a business office. Part of the seeming formality in London just comes from people going into their office, and then going on to places from there.
If you are going to a nice place, such as afternoon tea in one of the major hotels, or expensive restaurants, then even at weekends I would usually have a tie at least. And most others will be the same. I even did for a recent FT get-together one Saturday evening , and appeared to be the only one (although ajamieson came down from Scotland in a full kilt).
It's been a long time since I've heard of anyone being asked not to come in due to their clothing, and if that were to happen it would likely be due to teeshirts with inappropriate slogans on them, or that sort of thing.
Regarding Ireland - nothing required at all.
Oh, and if you do decide that hubby looks best with a tie, play the part yourself too, nice dress, high heels, etc. We guys do appreciate it!! (in fact that's often the reason why we say "I'd better dress up").