HMRC considers computer programmes and data of any kind as “Computer Software” (except items such as spreadsheets) eligible for capital allowances.
Software might be classified as capital expenditure where it may be expected to function as a tool of the trade for several years. So how long do you expect the website design to last? If it’s useful economic life is less than two years it is likely to be treated as revenue.
You may want to seek guidance from the website designers on its economic life and the more information you can provide the better (you do not give details of the nature of the website – other than it is a bespoke website – so it is only possible to give general principles).