Mate carnally in a teeming lunchtime tube? (10,5)

I believe the answer is:

alimentary canal

'lunchtime tube?' is the definition.
(passage which food travels down)

'mate carnally in a teeming' is the wordplay.
'teeming' indicates anagramming the letters.
'mate'+'carnally'+'in'+'a'='matecarnallyina'
'matecarnallyina' is an anagram of 'ALIMENTARY CANAL'.

(Another definition for alimentary canal that I've seen is " gut".)

I've seen this clue in The Independent.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.