How does a USA exchange like coinbase report back accounts to UK government?
They won't report back - they are barely even reporting anything to the US government.
(Note though that they seem to be routing credit card transactions through a foreign country rumored to be the UK.)
First of all, I don't think Coinbase own by US government. Its a company from Estonia.
Coinbase is a US based company headquartered in San Francisco.
Yes ,, sorry. I meant to say their Euro bank account in Estonia . Thanks for the clarification by the way.