As much as Trump is loose cannon, our trade was based on the USA being the 'importer of last resort' and many of the changes we're making are not THAT extreme compared to history, or compared to other developed nation's existing rules. Plus we are the ones choosing to make these changes.
With Brexit, GB has failed to make any sort of deal or even seemingly understand their negotiating position. The 'deal' they're eventually going to receive is 'having EU non-member rules forced upon them'.
Furthermore, even if the USA did the same thing and pulled out of all treaties instantaneously with no forethought or negotiation, we're a big enough economy that other countries would be forced to negotiate. Check out the comparison of US and UK economies. http://www.nationmaster.com/country-info/compare/United-King...
Britain appears to have gone with the intent of negotiating by political dogma.