Thanks for your question
For Tax purposes, these costs can only be offset against the capital gain that will arise if and when you sell the property (as an element of your house sale will trigger capital gains as you have used some of to run a business) so I am afraid the build itself, and any associated costs cannot be claimed against the trade income for tax purposes.
But you can claim the VAT on these costs as long as the sole purpose of the extension and build is for business purposes only (if there is some private element, then you will need to apportion the VAT reclaimed to reflect this)
So whilst these costs cannot be claimed against your self employment trade income for income tax purposes, note that purchases such as office furniture, and other office equipment/business equipment, can be claimed against the profits.
(And of course the VAT suffered here too can be claimed)
Do feel free to ask any follow up questions, but it would be appreciated if you would rate the level of service I have provided, as this ensures Just Answer pays me.