Well, Mr.Juncker said just before the referendum that if there was a Remain win there would be nothing further that Cameron could get in negotiations with the EU, no further whittling down on anything (and this likely helped the Exit side) but he may just have been trying a tough tactic. perhaps showing off that "if the Brits vote out, they won't be getting an easy ride either, so watch your step" .- without coming right out and saying it.
Maybe have to count in that some of the things politicians would be saying, in the UK and in Europe, will be more about position fighting or about trying to stick to a certain line than about their real limits to what they're gonna accept.
Also, I think Kythia had a very good point somewhere up this thread that there's no way the Commonwealth could really make up for the EU, not as trade partners, nor as political brothers on the world stage. Not in the short term anyway, let's say the next decade or two.