Lol, I knew this one would come up. Always happy to bust the myth...
For a start, postcodes are nothing to do with counties. Merseyside doesn't begin with 'L' and most of Cheshire, whether the modern incarnation or the larger traditional one, isn't in the CH postal area; as our most noted Cheshire gentleman, Paul Sidorczuk will attest to.
The letter on your postcode denotes the main head sorting office. 'L' meant the now defunct Liverpool sorting office on Copperas Hill in the city centre. 'CH' means the one in Chester. The number following it is the local sorting office that comes under the main one. It's purely an administrative device that helps the Royal Mail know which location to send its letters for sorting.
The Wirral/CH thing was the result of a fairly long term campaign by the Royal Mail to close the Liverpool sorting office. The Wirral mail would go via Chester whilst the rest of the 'L' would be taken over by Warrington. It took many years due to local political opposition and workers' unions. Eventually, they got their way and hiving off the Wirral to come under Chester sorting office was the first phase. The 'L' couldn't be kept as that would mean the mail still being sent to Liverpool; therefore the wrong head office. As the numbers used on the Wirral were on the high side and there were no CH equivalents, it was easy to just change L41 to CH41 etc.
A while passed, once more due to local political opposition and unions but the Royal Mail finally closed the Liverpool office only a few years ago. The 'L' designation was kept rather than changing to WA, as this would involve changing the numbers too i.e. as there was already a WA8, L8 would have to be WA[some high number]. That would've been controversial but also unnecessary. Anything with either an 'L' or 'WA' on simply goes via Warrington now.
Some snobby types on the peninsula may have been pleased; not so much because of any particular affinity with Cheshire so much as the belief that their car insurance premiums would go down, or even that their property would rise in value. The former patently hasn't happened and I see little evidence for the latter either. Even so, the idea that some people over the water were so upset about having an 'L' postcode that Royal Mail went out of their way to totally overhaul their sorting methods is, when you think about it, rather far fetched; absurd even.
--- old post above --- --- new post below ---
You're confusing administrative county with 'actual' county. Until 1974, Sussex was indeed considered a single county, even if it had two county councils. It had been since antiquity. Liverpool was never under Lancashire County Council but up until 1974, had also been considered a part of Lancashire since its establishment in 1207.