While I'm not here passing judgment on the efficacy of their vote --- frankly, knowing myself (a freedom fanatic), I suspect that were I a UK citizen I very well might've voted to leave (but certainly not to sever ties to the outside world) --- there's no question, per below, that British leaders are fully aware of the importance of international trade relations.
Here's from Tuesday's Bloomberg Economic Brief:
In the brief two months after the Brexit vote, U.K. Chancellor of the Exchequer Philip Hammond paid visits to Beijing and Hong Kong. Business Secretary Greg Clark headed to New Delhi. No surprise about what was on the agenda – expanding business ties. As Brexit throws the U.K.’s relations with Europe into confusion, strengthening links with Asian economies that are the main engines of global growth has seldom been more important.