There's also the issue of what the U.S. does. It is entirely possible the U.S. could put it's thumb on the scales by cutting a more favorable deal with the UK than with the EU, and that really would hurt because the UK and U.S. economies together are larger than the EU's.
Maybe it is this fear of the US, that will force the EU to try to be fair to the UK. Lets hope so.
The EU must be concerned about losing power. What other countries might decide to leave once the UK is gone?
The difference is that only 7% of British trade is with the USA, compared to 56% with other European countries