How formal is “Bless [him/her]”?

I am living in the UK, and I have recently started noticing quite a lot of people saying “bless [him/her]”, in contexts similar to:

— He has been doing poorly.
— Oh, bless him!

— She is so cute, bless her!

British dictionaries (Ox brigde) mention that this is informal language.

How informal is this expression, actually?

Out of curiosity: is it U or non-U? Would it be appropriate to say that at work (say, in an office/executive type of job), or is it too slang-ish? What does it show through (in terms of background) when one says it? Does it depend on the actual usage (e.g., OLD gives “Sarah, bless her, had made a cup of tea.” as another example)?