If you're not VAT registered, it really doesn't matter which way you do this. The end result is the same, whether you pay and are then reimbursed, or whether the company pays directly. There's no reason why the revenue would necessarily have a problem with this, as long as it's above board (i.e. the computer is a legitimate business expense and is used for your business).
If your company is VAT registered it's another story, as you will only be able to reclaim VAT on items invoiced to the company in the correct way.
(Note, I am not an accountant either, and you should consider raising this issue with your company's accountant, if you have one - which you really should).