Well, my views on comma usage recently have not always coincided with the recommendations of others, but since no one else has responded, I will venture an opinion that the first two would benefit from commas after the quoted material. Minor point: you ask about British English, but you have used the American spelling of "neighbor".
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GrammarholicLike this?When she asked "Where's the butter?", he said that it was all gone.When Alesia screamed "Help!", her neighbor called 911.Yes, that's what I had in mind.
GrammarholicI'm assuming that the last two are correct in BE with the commas inside;This is the usual convention in BrE for dialogue in w