Is the "shedule" pronuniciation just peculiar to my little patch of the country (Hampshire)? I always thought it was the usual British pronunciation, but everyone on TV says "skedule". Even the mighty Ray Mears.
'Sh' is the usual pronunciation in British English, whilst the 'sk' one is standard in American English. However, the latter - like many things American - has crept into our speech, too. An American comedian once made a joke of the difference by explaining that we were taught to say shedule in shool...his version of 'school'!
As QM says, the usual British pronunciation is [shed-youl], but the US pronunciation [sked-youl] is increasingly heard in Britain. As well as school, we also have scheme, schizophrenic and scholar - all pronounced with a 'sk'.