The phrase 'お言葉に甘えて' carries that uniquely Japanese nuance of humbly accepting someone's kindness while acknowledging their generosity. When translating to English, context is everything. In a casual setting among friends, 'Don't mind if I do!' works perfectly with that lighthearted tone when accepting an offer.
For more formal situations, 'I gratefully accept your kind offer' maintains the politeness. Business contexts might require 'With your permission, I'll accept' to preserve hierarchy awareness. What fascinates me is how anime localization teams handle this - the 'Spy x Family' dub used 'If you insist' during Yor's dinner invitation scene, which beautifully captured the original intent.