//..there have been widespread suggestions from certain camps that one way of addressing the huge disparity between the capital's sentiments on the EU and the rest of the country's, is to make London an independent city state. //
Yes, as I've said in other threads, the idea of London seeking independence is just slightly more sensible than Scotland doing the same.
Unfortunately for Londoners and the Scots (or at least those who voted to remain) they are both part of the only constituency that holds EU membership - the United Kingdom. The UK voted to leave and that's that.