Present president's take on English county (13)

I believe the answer is:

herefordshire

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

'english county' is the definition.
'herefordshire' can be an answer for 'county' (I've seen this before). I'm unsure of the 'english' bit.

'present president's take' is the wordplay.
'present' becomes 'here' (both can mean in attendance).
'president's' becomes 'ford's' (Gerald Ford).
'take' becomes 'hire' (synonyms).
'here'+'fords'+'hire'='HEREFORDSHIRE'

'on' is the link.

Can you help me to learn more?

(Another definition for herefordshire that I've seen is " County".)

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