I assume the self-inflicted part is leaving the common market / customs union... and rejoining this is not easy at all. I think it might be politically impossible for at least 10 years.
If the UK rejoined (assuming it was welcome after the last few years) I find myself wondering if forcing us (I'm British) to go all the way - into the Euro and onwards to full participation in everything - might actually be a good idea.
There are some aspects which taken in isolation may not be that great an idea (eg a Euro which includes such a variety of economies), but contrast that with the last approx half century where we've been the wall-fly. The one who goes to the dance, but hangs around the edges and never really joins in.
Half-hearted commitment can often be worse than none at all, and being forced to commit fully in order to be able to rejoin may well be the making of a better UK that takes it seriously and helps drive things forward.
Possibly.
Unless they change their minds in the meantime.
A trade deal with China looks unlikely given the current political climate. Trade deals with both the USA and India are fraught with political risk. The USA wants to be able to export GM food to the UK, out pricing UK farmers that were reliant on EU subsidies until recently. India is after a deal on immigration and this is even more contentious.
Trade deals will eventually be signed, however, almost certainly won't help to shorten or lessen the impact of the current recession.
(Not directing this at you, as I have no knowledge of what you consider low productivity to mean.)
What is often missed in the talk of low productivity is that the general assumption on hearing the phrase is that the problem is a lazy and unproductive workforce, which leads to the workers being an obvious target of blame.
In economics terms MFP is the more important view of productivity, and it's the amount of output that can be generated for a given set of inputs including not just labour but also capital/investment. And in general terms the largest issue here is not lazy workers but extractive management and asset-owners who take out the profits (as dividends, salaries, share buy-backs, etc) rather than reinvest them in the companies and the infrastructure. Without that investment the organisation remains below par for productivity as the inputs remain stagnant.
And that understanding shifts both the blame (and the required direction of travel to tackle the issue) to where it should be focused. Not pay, workers rights, etc, but addressing the inequality that allows that extraction which is the real cause of the productivity gap.