Gosh Mummy has gone all Brexiter with her capitals.
The EU doesn't hand back anything from a quota, it keeps the same terms of trade. We have to negotiate our terms, these are called schedules, each WTO nation has their own.
We will be allowed to trade without disruption if we keep to the same terms as the EU already has, if we wish to change them, then there might be disruption.
Yes we have more trade partners than the EU, but the EU is by far the largest trading partner. The USA with 15%, the EU is something like 45%, so more than treble that of our second largest partner.