It is an interesting question.  Obviously the normal perception is that you would have more negotiating power as a bloc, but if you are being represented by someone with trade priorities substantially different than your priorities, it might not turn out so well.  If you are from a "Fair trade philosophy" vs "Free trade philosophy" you will view any deal differently.

It also matters a lot on if you are a large consumer vs large exporter. 

For example, US trade priorities are typically supporting aircraft, weapons, beef and wheat exports, with a slight second tier for banking and insurance.  The rest are more or less tossed out there as pawns with no concerns for the effect on trade deficit, employment, or the budget deficit.

In the UK, the priority appears to be banking and insurance first, then weapons and sheep.  The rest are tossed out there for pawns.

Certainly Greece has not benefited from EU trade deals.

China protects it's entire business infrastructure core and is mostly focused on exports that bring in cash.  If any other country protected its business core to the level that China does, it would be called out and strung out.  They run the country like a business and for better or worse, have beaten out a lot of other countries in the process.

Taiwan has carefully protected its industries, especially the semiconductor industry until recently, and that is when it's problems really started.

Similarly, Japan has carefully protected it's industries from outside competition until the last decade or so and that is when it has met it's downfall.

As far as the UK and the US, a trade deal will be easy, as we more or less think of the UK as our weird but likable uncle.  The deal will only be complicated by UK banking regulations, and the US is right now moving to match these. (for better or worse)

The bigger challenge the UK faces, IMHO, is that it is no longer a critical mass.  They tried to play both side of being part of the EU and being a bridge for China to more easily enter the EU markets and now with Brexit, this falls apart.

The risk is that the UK ends up being pulled too far under the influence of China and is eventually forced to be part of China's sphere of influence, obvious or not.  With the current tax structure oriented toward VAT vs a sales tax, I don't see how this will change.

I am just an ordinary guy though, so those might be completely useless personal opinions.