It's pathetic that you have to ask who the one leave party in the UK is. Could it be the LibDems, who are remainers? Could it be Labour, who are remainers? The Conservative Party, who are remainers? Hmmmm, who could the only leave party possibly be?
The referendum was a binary question: leave or remain.
There is only one type of leave, since remaining in any capacity constitutes a type of remain.
Leaving does not involve a deal (treaty), since the question was whether to leave or remain. Treaties are a separate matter.
There are not different methods of leaving. There is no such thing as "how" to leave.
There is only leave.
Leave the EU > trade with EU and cooperate with the EU > any treaty agreed with the EU after leaving must keep us out of the EU. That's how simple it is.
Simple, of course, if our politicians did their jobs and carried out the instruction given to them.
Gerard Batten wrote a book, before the referendum, about how to leave the EU, and detailed how simple it would be to leave. It's an extremely simple thing to do as long as the people tasked with doing it, want to do it.