Liars busy travelling to Cathedral city (9)

I believe the answer is:

salisbury

I'm a little stuck... Click here to teach me more about this clue!

'cathedral city' is the definition.
'salisbury' can be an answer for 'city' (Salisbury is an example). I'm not certain of the 'cathedral' bit.

'liars busy travelling' is the wordplay.
'travelling' indicates anagramming the letters.
'liars'+'busy'='liarsbusy'
'liarsbusy' anagrammed gives 'SALISBURY'.

'to' acts as a link.

Can you help me to learn more?

(Other definitions for salisbury that I've seen before include "See" , "Building in favourite English view" , "Former name of capital" , "prime minister" , "City on the Avon" .)

I've seen this clue in The Independent.

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