The British government are after him because, after he was allowed to enter the country and having gone through due process, his European arrest warrant was uph

The British government are after him because, after he was allowed to enter the country and having gone through due process, his European arrest warrant was upheld and he absconded. That has nothing to do with state secrets and, so far, the US haven't asked for him to be extradicted. As the US has the concept of a closed warrant,it's not currently possible to know if he's wanted by them. It's not exactly inconceivable.