The first hop would go from "my UK client machine" -> "my VPN server elsewhere" which would impede Mullvad from automatically recognize you as a UK customer because that "server elsewhere" wouldn't have a UK IP address.

The second, Mullvad, hop would go from "my VPN server elsewhere" -> "some other IP maybe in yet another country"

As long as you didn't pay with a UK payment system (so, use a crypto currency or send them money in an envelope), due to that first hop Mullvad would have no way to know you are British and thus no legal obligation to treat you as such.

However a "my server elsewhere" also needs to be paid for. Further, all connections from that server would always be yours since you would be the single user of that server. Adding a Mullvad hop after that adds the anonymization of, for the rest of the Internet, your stuff being just one amongst many connections from many Mullvad clients coming from that server, plus Mullvad is probably much better at anonymizing stuff that "random techie setting up their own a VPN server on a VPS", plus if you pay Mullvad using an anonymous payment system, they themselves have no idea who you are if they were ever legally forced to disclose it.

That first hop gives Mullvad plausible deniability about serving a UK customer without ID, whilst the second hop gives you a stronger anonymity than you would get if your entrance point into the internet was a single-user server you owner or rented.

Mullvad also accepts anonymous cash payments, good luck with identifying me as a mullvad user with only an envelope, a target address,an account id which isn't tied to a name and 10 bucks in it.

I think you are overestimating the threat model. Nothing is ever fool proof but Tor does make it extremely difficult to actually identify someone. You are talking about a hypothetical attack vs something that is actually feasible to pull off. Tor is design so that there can be many compromised nodes without to much danger. Tor's popularity as makes it hard to track individuals since there is a lot of traffic.

...have you ever used it?