Predatory reptile in cold air swimming without company (11)

I believe the answer is:

crocodilian

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'predatory reptile' is the definition.
'crocodilian' can be an answer for 'reptile' (crocodilian reptile is a kind of reptile). I am unsure of the 'predatory' bit.

'in cold air swimming without company' is the wordplay.
'swimming' indicates an anagram (letters swim around into a new order).
'without' is an insertion indicator ('without' can be similar in meaning to 'outside').
'company' becomes 'co' (abbreviation).
'in'+'cold'+'air'='incoldair'
'incoldair' with letters rearranged gives 'crodilian'.
'crodilian' enclosing 'co' is 'CROCODILIAN'.

Can you help me to learn more?

I've seen this clue in The Times.

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