Hello, I am Keith, one of the experts on Just Answer, and pleased to be able to help you with your question.
Well, yes you can, but you will be liable for Income Tax (IT) on the rent received. The whole proposal seems over complex. Just use the Annex for business and charge all expenses thereof to the same leaving a surplus which will be liable to IT.
That is the rough and ready twist of the spoon to stop the treacle running off so to speak and by far the easiest way to manage the matter. If HMRC insist on the conversion costs being a capital allowance matter it will not make the slightest difference as the Annual Investment Allowance (AIA) under that regime is at 100% anyway.
I do hope that you have found my reply of assistance.