”.’ and .”’ endings in BrE

John said, ‘I hate when he called me a “schlimazel”.’
(Is ”.’ the proper ending punctuation when we're referring to a word as a word in BrE? I think it may be.)

Mike said, ‘I overheard Daphne say, “Howard is fatally ill.”’
(But, would we use the ”’. ending per BrE in the example above?)

Please, no recasts to reported speech.

I thank you for any input.

Michael G.