For a private company, you have 9 months from the accounting reference* date to file your annual accounts with companies house. You have 9 months 1 day to pay your corporation tax 12 months after your company year end.
If you file small audit-exempt accounts, you may be able to jointly file accounts with both Companies House and HMRC.
* Companies House gives your company an ‘accounting reference date’ when you set-up your company - this is when they expect your company’s year end to be (e.g. it’s the last calendar day of the month your company was set up).