Charge one politician with a piece of treachery (7)

I believe the answer is:

impeach

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'charge' is the definition.
(I know this)

'one politician with a piece of treachery' is the wordplay.
'one' becomes 'I' (Roman numeral).
'politician' becomes 'MP' (Member of Parliament).
'with' is a charade indicator (letters next to each other).
'a piece of treachery' becomes 'each' (I can't justify this - if you can you should give a lot more credence to this answer).
'i'+'mp'+'each'='IMPEACH'

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(Other definitions for impeach that I've seen before include "Charge with major crime" , "Arraign, charge" , "Arraign - revile" , "Charge public official with misconduct - Clinton?" , "Charge with treason, etc" .)

I've seen this clue in the Evening Standard.

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