The UK exited the EU but retained one of the most active Bitcoin retail markets in Europe — FCA-registered crypto-providers serve ~3M holders. The .uk TLD is the modern English-market signal (replacing the older .co.uk pattern). UK-Bitcoin retail expansion plays favor .uk over .com for local-trust positioning.
The United Kingdom is one of the largest Bitcoin markets in Europe and it sits outside the EU regulatory perimeter, which makes it a separate go-to-market rather than an extension of one.
.uk is the short form that has largely replaced .co.uk in new branding. For an international Bitcoin brand it is the defensive purchase that stops a UK operator from launching under a name the brand already uses everywhere else.