A new deal. What we're doing currently doesn't work so the UK needs to innovate - as we do so well.
Australia's Operation Sovereign Borders has worked fantastically well, bringing boat arrivals down from roughly 20,000 people in 2013... to a single boat in 2014. In just 1 year. They combined turn backs at sea, immediate detention, no settlement for anyone who had arrived illegally, and third country processing in Nauru and Papua New Guinea.
Before you cry that Nauru and Papua New Guinea are too far away (well, duh!), the Group of Five Initiative - Germany, Austria, Greece, Denmark, and the Netherlands - have been working on deals with Rwanda, Uganda, and Uzbekistan to privide third-country facilities for failed asylum seekers.
It's not too big a stretch to suggest that we combine the approach that worked so well for Australia - including third country processing - (coming out of any agreements stopping us) with the actual countries which are geographically appropriate for Europe... and who still seem keen.