At intervals, went round educational establishment (4)

I believe the answer is:

eton

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'educational establishment' is the definition.
The definition suggests a singular noun which matches the answer.

'at intervals went round' is the wordplay.
'at intervals' indicates alternate letters (letters are taken at regular intervals).
'went'+'round'='wentround'
The alternating letters of 'wentround' are 'ETON'.

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(Other definitions for eton that I've seen before include "School near Slough" , "Public school near Windsor" , "Kind of collar or jacket (worn at college?)" , "collar, perhaps?" , "Note sent up to English public school" .)

I've seen this clue in The Independent.

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