If the annex has its own entrance (regardless of having a connecting door) and has its own self contained facilities, Kitchen and bathroom, it probably should already be classed separately for CT.
https://www.gov.uk/rent-room-in-your-home/the-rent-a-room-scheme
The Rent a Room Scheme
The Rent a Room Scheme lets you earn up to a threshold of £4,250 per year tax-free from letting out furnished accommodation in your home. This is halved if you share the income with your partner or someone else.
You can let out a room or an entire floor.
How it works
The tax exemption is automatic if you earn less than the threshold. This means you don’t need to do anything.
You must complete a tax return if you earn more than the threshold.
You can then opt into the scheme and claim your tax-free allowance. You do this on your tax return.
You can choose not to opt into the scheme and instead record your income and expenses on the property pages of your tax return.