The UK is (currently) the world's 5th biggest economy.
And going down...
So we are worth having a deal with. Especially if the US, China, and EU are being too intransigent (which they are). The US is, well, Trumpian. China is more interested in deals that see it dominate, not partner. The EU imposes a ton of burdensome rules, and isn't interested in explaining why the principal of free movement of people won't get extended to cover countries it might want a trade deal with outside of the European continent.
I agree that a Trump US is anti free trade, but you ignore a number of things. Firstly is geography. Even in a global market it makes more sense for say Australia to align itself with SE Asian markets on its doorstep. Population size, the EU is a much bigger market meaning it is easier to align standards etc. All countries have rules, but the bigger you are, the more economical it is to align to them. Again UK customer base is to small for that to make sense.
Lets also not pretend the UK has any interest in extending freedom of movement...
For example Japan and the UK seem to be becoming very cosy, a number of defence treaties have been signed in recent years.
I see no evidence for that. Japan has always liked the UK because it provided a gateway to european markets. Japanese buisnesses are generally flabbergasted that it is about to leave the EU
There's the TPP agreement that has gone ahead without the USA. That would be a good one to get in on.
It's all madness really. There's a good chance the EU will collapse under the weight of its own corpulance. France and Germany weren't too happy with the latest budget inflation being demanded by the EU commission (20% ish).
That's the brexit dream isn't it. The UK will leave and drag the rest of Europe down to its level. Except it isn't happening. Support within the EU for the project has increased with the referendum. There will always be arguments within the EU and challenges, but that does not mean there is any appetite for a breakup of the EU generally
Can you imagine a democratic government getting away with 20% tax increase across the board?
You do know that the EU has a parliament that is democratically elected and the commission consists of representatives of democratically elected governments don't you?