Employment solicitor here.
You are entitled to give more than one month’s notice. The notice period is the minimum you must give. So, in theory, you could give a years notice.
As some have said, that doesn’t stop your employer dismissing you in that period. However, if you have two year’s service, they must have a fair and lawful reason (conduct, capability, redundancy, etc…) and follow a fair process when doing so.
if I’ve been working for a business for one year and decide to give a year’s notice (rather than one month in my contact), the employer could say, fair enough, but as you’re not committed to working here, you’re sacked on one month’s notice.
That would be more difficult for the employer if I had two years’ or more service. However, the could still potentially fairly dismiss for some other substantial reason (as it’s called in law) stating that my lack of commitment to the job (eg that they didn’t want to spend a year investing in me with training, experience, etc..) when I’ll leave at the end of that year.
So I don’t think you’ve got a lot to gain by giving a longer notice, but if you are, I would wait until you’ve got two years’ service before doing so.