Parched? Then swallow one drink (3,7)

I believe the answer is:

dry martini

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

'parched? then swallow one' is the wordplay.
'parched?' becomes 'dry' (similar in meaning).
'then swallow' becomes 'martin' (martin is a kind of swallow. I am not sure about the 'then' bit.).
'one' becomes 'i' (Roman numeral).
'dry'+'martin'+'i'='DRY MARTINI'

Can you help me to learn more?

(Other definitions for dry martini that I've seen before include "drink" , "Gin-based cocktail" .)

I've seen this clue in The Times and The Telegraph.

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