Sole Traders / Partnerships.  If the computer is purchased for part business/part private, then the business portion of the cost can be claimed.  VAT claimed back on the purchase must be in the same proportion.

Limited Companies. The full cost of the computer can be claimed if the sole, or a significant, use of the computer is for the business, and private usage is only incidental.

If it is bought mainly for private use and only used minimally for business, the full cost can still be claimed, but the person (director or employee) using it must pay income tax on 20% of the cost of the computer (called a benefit-in-kind).  This should be recorded on a form P11D (or possibly on the payroll), and HMRC will then amend the person’s tax code.