Move to a more upmarket café (7)

I believe the answer is:

tearoom

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

'upmarket cafe' is the definition.
'tearoom' can be an answer for 'cafe' (I've seen this before). I am unsure of the 'upmarket' bit.

'move to a more' is the wordplay.
'move' is an anagram indicator (I've seen 'moving' mean this).
'to'+'a'+'more'='toamore'
'toamore' is an anagram of 'TEAROOM'.

Can you help me to learn more?

(Other definitions for tearoom that I've seen before include "Cafeteria" , "Small cafe" , "24" , "Place for light refreshments" , "Restaurant for light meals" .)

I've seen this clue in The Times.

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