The short answer for your situation is yes — as a VAT-registered business selling pre-recorded courses to UK customers, you should be charging the standard 20% rate. But your question about the education exemption is a good one, because this is a common point of confusion.
The education exemption
An exemption for education does exist, but it is much narrower than most people expect. It applies to supplies made by 'eligible bodies' — schools, universities, colleges, further education institutions and certain non-profit bodies — as set out in HMRC's VAT Notice 701/30 on education and vocational training. A commercial business selling its own courses is not an eligible body, so its course sales are standard-rated. Being a business rather than a school or college is precisely what keeps you outside the exemption, not a technicality.
Pre-recorded vs live
It makes no difference here. The test is about who is making the supply, not the format. Whether your courses are live webinars, pre-recorded videos or downloadable PDFs, a commercial provider charges 20%. In fact, pre-recorded downloadable courses are treated as electronically supplied (digital) services, which are firmly standard-rated when sold to UK customers.
Overseas customers
This is where it does change — but not in a way that helps the UK position. For business-to-consumer supplies of digital services, the place of supply is where the customer belongs. So UK customers mean UK VAT at 20%. For customers outside the UK, UK VAT generally does not apply, but you may need to account for VAT in the customer's country instead (for example, EU consumer sales may need to go through the non-Union OSS scheme). If you sell business-to-business overseas, the reverse charge often applies. This is worth getting right before the overseas side grows, because the evidence you need is proof of where each customer is based — two pieces of non-contradictory evidence, such as billing address plus IP location or bank details.
Practical invoicing
Charge 20% on all UK course sales and show it clearly on the invoice. Keep records of customer location for every sale, because that determines the place of supply. And double-check your checkout or payment platform is applying VAT by customer location automatically — many course platforms can do this, but the settings need to be right. If your course business grows quickly, watch your VAT position on the cross-border side; a one-off review with your accountant before you scale internationally will be money well spent.