Alarm cable near ac mains cable?

Hi All.
I've very nearly finished installing a wired alarm system in my house and have now just read the instruction manual..... I know I know, what can I say, I was too keen, I'm a bloke etc etc...
Anyway, it says not to run any alarm sensor cable alongside mains supply cable which I have done everywhere including under floors. It would be a huge job to reroute it all so can anybody offer an opinion on how necessary it is to have the cables kept apart?
Many thanks.
Jim, London UK.