Any particular countries?
Japan would probably jump at a free trade agreement. After all we send less to them than they send to us. And the japanese goods would be cheaper to the consumer here (or at the same price but with a bigger margin for the japanese seller). However, for every million of japanese imports import duty is charged to the tune of £200k by the government. Say Japan exports £5bn to us annually. That is a billion in tax revenue gone. And those are finger in the sky figures, and I would imagine Japan actually sends us a HELL of a lot more than that.
USA - as explained earlier. Obama has said no. Clinton has said no. Trump has said yes. Trump is second favourite in a two-horse race. Again, if that happened it would actually benefit them more than us as we are gross importers. And again, a shedload of tax revenue gone.
As you say we do have a better economy than much of the world. However, most of our economy is based on financial services these days. We are THE key banking area in Europe. We are THE main stock exchange in Europe. If that all shifts to Frankfurt for the banks, and to Paris for the Bourse we have a serious problem. We are not a manufacturing economy and haven't been for decades.
If France and Germany take the financials we become the sick man of Europe, and lo and behold, the EU hardball will have worked.
As the economy contracts due to the above, the pound will then collapse further and it will NEVER recover. Money men or otherwise. We will stabilise as by far a much weaker economy.
But hey, we will be able to tell Johnny Foreigner to sod off, though.