You still are.
When the boundary changes came in ( I think it was 1974),
They are political boundaries not historical ones.
When I was living in Warrington I always put Lancashire in my address, even when renewed passport,
At one time as you drove out of Warrington along the A49 or A56 towards Stocton Heath And Walton there was a sign saying Cheshire on the other side of the Swing bridges over the Ship Canal. Same as if went over the bridge on the A50 going into Grappenhall.
The boundary for Lancs and Cheshire was the River Mersey and the Ship Canal.
Put Cheshire in your address and you will still get your mail.