Meaning of “if you don't mind me saying/asking” in the English Dictionary

british dictionary

"if you don't mind me saying/asking" in British English

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if you don't mind me saying/asking

used in order to be more polite when you say something that could slightly upset, annoy, or embarrass someone:

If you don't mind me saying (so), I think the soup needs a little more salt.
Do you have a boyfriend, if you don't mind me asking?

(Definition of “if you don't mind me saying/asking” from the Cambridge Advanced Learner’s Dictionary & Thesaurus © Cambridge University Press)