Employment Law - no contract provided

[Barquentine]

If a signed offer letter says one month's notice on either side is required to terminate, rising to 3 months after one year, and then the employer never provides a contract - do those terms signed by both parties in the offer/acceptance acknowledgement prevail - i.e. does one have to give 3 months' notice to leave?

[buildersmate]

You do have a contract - the signed lettter forms part of it. The other parts are any policies or a Company Handbook, and 'custom and practice' - namely what your employer has done before.
So technically you are obliged to give 3 months notice.
But your employer is in breach of employment law if he has not provided you with a written statement of your main terms - which is what you are probably calling a 'contract'.