And nobody is going to sign a trade deal with the UK until they know what the arrangement is with the EU - Japan has said as much for starters, and despite what Trump says, the US won't even countenance an agreement that places the GFA in jeopardy. Also the countries and trading blocs that the EU currently have an arrangement with, and from which the UK is withdrawing, will have clauses written into them (most likely drawn up by British lawyers) forbidden third countries from having a more favourable agreement. So yes, in theory 'we can sign what we like with anyone', but in practise that means the Faeroe Islands and the Palestinian Authority at the moment.