Fusty outdated place for travellers built on Garrick's image (7,8)

I believe the answer is:

smoking carriage

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'fusty outdated place for travellers' is the definition.
I can't judge whether this defines the answer.

'built on garrick's image' is the wordplay.
'built' indicates anagramming the letters (the same letters can be used to build the answer).
'on'+'garricks'+'image'='ongarricksimage'
'ongarricksimage' anagrammed gives 'SMOKING CARRIAGE'.

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I've seen this clue in The Independent.

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