If the UK rejoins the EU will push for full integration, no half-in/half-out relationship like before. This will mean Euro and all. I actually fully support this idea but others might not.
What remain and leave could both agree on before the referendum was that the EU was and is a lumbering, beaurocratic behemoth badly in need of some internal reforms.
Had David Cameron had any foresight he would have campaigned for this prior to the Brexit vote and instead of Brits being sold this lie about being 'oppressed by the EUSSR' and allowing the fringe elements of politics to take hold we could have led from the front and allowed ourselves to take a place at the front of the pack.
Britain wrote most of the maastricht treaty that forms the basis of the EU (back when we had a sensible sense of politics) and they could have leveraged this and put the idea of Brexit to bed forever.