Redhead's accompaniment at tea?

I believe the answer is:

gingernut

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'tea?' is the definition.
Both the answer and definition are singular nouns.
Maybe you can see an association between them that I don't see?

'redhead's accompaniment' is the wordplay.
'redhead' becomes 'ginger' (I've seen this in another clue).
'accompaniment' becomes 'nut' (I am not sure about this - if you are sure you should believe this answer much more).
'ginger'+'nut'='GINGERNUT'

'at' is the link.

Can you help me to learn more?

I've seen this clue in The Daily Mail.

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