In any case the UK has been left out of the negotiating room: the deal will be signed by 23 Member States, with others considering whether or not to sign up. Backing out of a deal was always going to upset the Eurozone countries, but it will be interesting to see how the UK's relations will develop with the other non-Eurozone countries. Sweden's foreign minister mocked the UK's position in a tweet:
"Worried that Britain is starting to drift away from Europe in a serious way. To where? In a strong alliance with Hungary."
The inclusion of these other non-Eurozone countries should be enough to ensure that the Eurozone doesn't go ahead on internal market matters without the rest of the EU (the Danish presidency will be particularly helpful in protecting the position of non-Eurozone members), though it probably does damage the short term influence of the UK in the EU.