Just to add my two penn'orth. The battery on my Dyson V8 packed in back in May 2019 and I bought a knock off from Amazon. It wasn't the cheapest by far at £54 either.
However it didn't work, I just got error lights on the vacuum so, I returned it for a full refund. Good old Amazon.
I then found someone selling genuine Dyson batteries for £98 on Amazon but before pulling the trigger on the purchase I thought I'd just check on the Dyson website to see what their extortionate price was.
However, you cannot buy a battery online directly from Dyson, they request that you ring them to discuss the issue you are experiencing. So, I did and I spoke to a very knowledgeable guy who asked me about the problem I was having with the battery. He explained that sometimes it isn't a battery but a filter or switch problem and they didn't want to sell batteries to people who didn't need them.
Anyway, he agreed that my battery was on its last legs. So, I asked him how much a replacement would be and held my breath in anticipation. Imagine my total surprise when he announced that a new battery, with next day delivery and a thirty day return window, if not totally satisfied would be £65!
Needless to say, I nearly bit his hand off. The battery arrived, as promised the next day and is still going strong.
I did actually email the seller on Amazon and asked them why they were selling the battery for £33 more than Dyson and they replied saying that they were in short supply and Dyson themselves hadn't got any, really!