Of course they are negotiated as a bloc, negotiating on behalf of a market of 500 million people is a lot stronger than on behalf of a market of 60 million people.
But that's not the point. Why would Britain suddenly improve trading with the Far East when it leaves the EU? Plenty of EU members outperform the UK when it comes to international trade (both with the Far East and with other parts of the world) so the current trade agreements are not the reason why Britain performs poorly.
Britain just needs to get better at producing goods or services that people in other countries want. Until it does that I don't expect Britain's current account deficit to significantly improve, with or without Brexit.*
* Of course, leaving the EU is projected to reduce the value of Sterling by about 15 - 20% but I'm not a firm believer in devaluing currency for the benefit of the medium or long term. The effects are only temporary and, worse still (look at how Greece got into its current mess, devaluing the Drachma instead of structurally improving the economy – until its eurozone membership put a stop to that trick), devaluation tends to kick the can of structural improvements down the road.