Crossword Genius

Heard drift, swell, immediately (8,3)

Ross

I believe the answer is:

straight off

I'm a little stuck... Click here to teach me more about this clue!

'immediately' is the definition.
(I've seen this before)

'heard drift swell' is the wordplay.
I cannot quite understand how this works, but
'swell' could be 'toff' (wealthy or high-class person) and 'toff' is found in the answer.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for straight off that I've seen before include "Without hesitation or deliberation" , "Immediately" .)

I've seen this clue in the Sydney Morning Herald.
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