With a little gulp, swallowing a tea cake (6)

I believe the answer is:

gateau

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'cake' is the definition.
(gateau is a kind of cake)

'with a little gulp swallowing a tea' is the wordplay.
'with' is an insertion indicator.
'little gulp' becomes 'gu' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'swallowing' indicates putting letters inside.
'a' going inside 'gu' is 'gau'.
'gau' placed around 'tea' is 'GATEAU'.

Can you help me to learn more?

(Other definitions for gateau that I've seen before include "Creamy dessert cake" , "rich food" , "Richly decorated cake" , "Fancy cake" , "Cake (from the Black Forest?)" .)

I've seen this clue in the Evening Standard.

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