Crossword Genius

Picked up homeless aristocrat without hesitation (8,3)

Ross

I believe the answer is:

straight off

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

'without hesitation' is the definition.
(I've seen this before)

'picked up homeless aristocrat' is the wordplay.
I cannot really see how this works, but
'aristocrat' could be 'toff' (toff can mean an upper-class person) and 'toff' is found in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

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

I've seen this clue in The Telegraph.
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