This question comes up a lot on social media and I always have a very simple answer to it: no. However, the question does deserve a longer answer, explaining why exactly that is. Consider this as the sort of foreword to a longer piece that would explain everything in detail; this is my macro view of why it wouldn’t fly, in other words.
First let’s take the wealthier countries within the Commonwealth, the ones who have economies whose size are at a commensurate level with Great Britain’s. So Canada, Australia, New Zealand. All I’ve ever heard from anyone connected to any of these three countries at official levels, whether they be diplomats, politicians form the right or the left, is that seriously, you must be joking. Australia and New Zealand have their own regional interests to work with and aren’t taking trade with a country that is literally on the other side of the globe as being a high priority. Canada I know even more about, having grown up there. Brits who have spent little or no time in Canada really do not understand Canadian attitudes towards the UK. First there are the ex-pat Britons or the children of ex-pats, who are large in number. Most of them are people who left Britain with a chip on their shoulders and while they tend to be anti-European instinctively, they aren’t in a hurry to help bail Britain out of a situation “they bloody made themselves when they rejected the Commonwealth for the bloody French” (that is a genuine ex-pat quote, incidentally).
Those Canadians of non-British ethnic origin find the attachments to the UK alienating; they take it as a slant on their claim to be fully fledged Canadians in some sense (this is particularly prevalent with people of eastern European descent, in my experience). Amongst both groups, the idea of a trade deal with Britain is slightly scary and not very appealing – usually for much the same reason, actually. Given the large ex-pat communities and their willingness to pay exorbitant amounts for British goods, a level playing field for British goods in Canada gets protectionist backs up. In fact, I think Canadians would be much more open to a Canada-EU free trade deal if Britain left the EU – cheap French wine and German cars sounds appealing, while having your domestic cheese market wiped out by the Brits, not so much.
So the rich countries in the Commonwealth aren’t in any hurry to do a deal with a suddenly single Britain. And that’s a huge problem – trade deals are by definition done between two willing partners. If one really, really wants to do a deal and the other isn’t fussed, it puts the one who isn’t bothered in a prime negotiating position. If they’re bothered enough to even begin talking about it all, at least.
Then we come to the developing portions of the Commonwealth. Imagine Britain trying to do a free trade deal with India or Pakistan as a matter of urgency. What’s on offer? Surely not free movement of people. But even a relaxation of immigration standards between the countries could be tricky for Britain to swallow. As for goods and services: for those of you still going on about the scale of Polish immigration this past decade and its impact of working class jobs, you should really consider how many jobs could go to southeast Asia if we relaxed the barriers even further in this regard. This is mere speculation, obviously – like everyone else in the universe, I have no idea what Brexit means either. I’m simply going by what I see in front of me.
India and Pakistan face vastly different challenges than Britain does over the next quarter century. To the Outers, I direct you to the likes of Portugal and Greece being in the EU and how you have at times rightly pointed out that France and Germany being in a monetary union with countries with much smaller economies was bound to create problems. So a free trade agreement between developing nations with huge populations and the UK would be smooth sailing then? History doesn’t provide us with comforting comparisons on that front.