They add a markup of 5%, taking it to £1.05
Then they add 20% vat, taking it to £1.26
The final customer pays the VAT, which is collected from the OP. They reclaim VAT on things they buy, not things they sell.
I still don't understand how just re-selling something at a profit is 'adding value' in VAT terms. I thought the 'value' added was not monetary but actually doing something to the product(s) to make them more valuable.
This is effectively the same as a sales tax; just the mechanism for collection is different.
For service-orientated businesses, the mechanism is the same; the terminology just makes less direct sense. In general, a business still get to reclaim all the VAT it pays on stuff it buys, and must charge VAT on all the stuff it sells.
I find the definitions in the investopedia link you provided very confusing.
Essentially becoming VAT registered turns you into a tax collector :-)
If you do something to the product, that only adds value when you sell it for more than it was worth before.
Adding value to something can be as simple as buying it in a time when no one needs it, and selling it when everyone wants it. Basically you added value by carrying risk or storing the asset.
In essence, the unstated assumption is that if you bought it at $1 then it had a value of $1; and if you sell it at $2 then you added value, and we don't need to know how that value was added. Did you improve the item itself? Did you move the item where it was needed more? Did you offer it to customers who weren't served by others? Did you advertise&market the item to make it more attractive? These all are valid means of adding value.
Assuming you found a company selling Bitcoins and charged VAT you'd pay £1.20 but claim 20p back from HMRC therefore the total cost would be £1.
Then same same calculation that is in the post you replied to applies. The customer would end up having to pay £1.26 of which ~21p would be payable to HMRC, leaving you with ~6p profit. But who is going to pay £1.26 for bitcoins when you can buy them for £1.05 elsewhere? If the UK based company sold them for £1.05 they'd be losing money every time they sold them due to the VAT they'd owe to HMRC.