Hugh Grant -- Got (Breast) Milk?!

Hugh Grant knows ... it's rude to interrupt someone during a meal ... so he did his best not to bother this suckling baby during a photo with a fan.

The pic was shot this weekend at the Castle Inn pub in Dover, England -- which features "Pudding Day" on Wednesdays and Thursdays.

We're told the woman in the pic is the pub owner's wife -- who clearly had no problems whipping out her baby feeders inside the establishment.