Yes, the company can pay for it directly — and on your facts the tax treatment should be favourable. But you are right to focus on the "related to the business" test, because that is what decides everything.
Corporation tax. The cost is deductible as a business expense if it is incurred wholly and exclusively for the purposes of the trade. A bookkeeping and accounts course that helps you run your design company — understanding your own management accounts and keeping proper books — clearly meets that test. If, by contrast, the training enabled you to start a wholly new trade or profession unrelated to the company, HMRC would treat it as a personal cost and deny the deduction.
Benefit in kind. Training paid for by the company can in principle be a taxable benefit, but there is a specific exemption for "work-related training" (section 250 ITEPA 2003). Training counts as work-related if it is designed to impart, instil, improve or reinforce knowledge, skills or personal qualities likely to be useful to the employee in performing their duties, or to qualify or better qualify them to do so. Your course fits squarely within that, so there should be no benefit-in-kind charge and no Class 1A NIC.
How strict is the test in practice? HMRC generally accepts training connected with the employer's business, even where the employee also gains transferable skills. The red flags are courses clearly for personal interest or a new career. Document the business purpose — a short board minute noting why the course benefits the company is sensible.
Practically: have the company pay the provider directly (invoice made out to the company), keep the course details and receipt, and claim the £2,500 plus exam fees as staff training costs in the accounts. On these facts I would expect no personal tax consequences for you at all.
