I would say co-operate in a number of areas like security, intelligence & policing, research. Brexit is (to use a phrase of Churchill's) not the beginning of the end but the end of the beginning. It's not the end of our relationship with Europe but the beginning of a new one.
The truth is that the EU is a collection of vested interests, where the Germans controlled the finances, to the detriment of most other countries (particularly in Southern Europe). The French were happy to tag along because they had the sop of the wasteful Common Agricultural Policy. It's done nothing to halt increasing authoritarianism and de-liberalisation in Poland & Hungary.
The Common Market was an excellent economic idea but the French & Germans had delusions of grandeur and wanted a vanity project involving increasing political and monetary convergence.The Euro is a sticking plaster covering up all sorts of monetary and fiscal issues. Freedom of movement was another piece of economic illiteracy, which just allowed the redistribution of scarce labour market skills (and therefore potential tax revenues) from poorer countries to richer ones.
I'm not claiming that being out is all sweetness and light by any means but at least we'll be hopefully doing things for positive reasons rather than deciding that this or that latest EU requirement isn't for us. I've always said I'd rather we were out, with one foot in, than in, with one foot out.