No Warrington isn't part of Cheshire. Its a Unitary Authority Now.
Cheshire only really exists on maps as something of a historic entity.
Cheshire Council was abolished some years ago. Its now Cheshire East and Cheshire West and Chester, with bits in Halton and Warrington.
There was talk of a singular Cheshire Area like the Liverpool or Manchester Mayoral Region but Cheshire east and Cheshire west couldn't agree with Warrington over it, as there was a feeling of too much difference and not enough common ground.
Warrington USED to be part of Cheshire.
Historically the North of Warrington WASN'T Cheshire though. North of the Mersey was originally Lancashire. You still occasionally come across people from Warrington who refer to it as part of Lancashire.
Then it became Cheshire.
And its still part of Cheshire when it comes to Crime. It falls under Cheshire Police.
Confusingly this gets partly funded out of the Liverpool City Region as Halton is part of it but is Cheshire Police.
Then Halton and Warrington share a NHS trust. Which gets some funding out of Merseyside.
Then there are the parts of Warrington which didn't use to be parts of Warrington and were parts of long abolished separate boroughs. Which were very very rural Cheshire.
And the bits of Warrington South that are apparently no longer going to be part of Warrington for General Election purposes but will be part of Tatton Constituency instead due to boundary reviews.
And yes Altrincham and Hale in Trafford are WA14 whilst Knutsford in Cheshire East is WA16.
To be an authentic Cheshire Housewife you really need to live in WA16. Cheshire Housewives don't live in Winsford anymore than they live in Warrington... Ewww no.