I've always interpreted the 'being close' line as 'having a strong bond with someone' because of the 'ain't like being true': one may think someone is a friend of theirs, but this person does not care at all about them, which I think is the case: he means that Sweeney's feelings for Mrs. Lovett are a sham.
Just my interpretation :)
And, morosco, to answer your question, here are some people pronouncing the word 'been':
http://pt.forvo.com/word/been/#en . Eveningstar, who is from Canada, also pronounces it like 'bean'. Toddmichael, who's from Australia, pronounces it the same way. But, yes, people with british accent pronounce been like bean.
Updated On: 5/19/14 at 11:05 AM