Looking at how Belgium prevented the EU from having a trade deal with Canada, suppose the next trade deal with the US is to be signed after article 50 was invoked- could the UK prevent such a deal from going ahead?
That is the whole issue behind the "no talks before article 50 is invoked" rule.
If talks were allowed, at any time the UK would be able to use the leverage of blocking the internal politics of the EU to get whatever it wanted.
Once art. 50 is invoked, there is a time limit. It means any blocking action by the UK will have due date, and that the EU will have the leverage of simply "letting the UK go" without any concessions after the two years, in case that the UK becomes a PITA.
Then the follow up question is "why would the UK invoke art. 50 if it means giving away this advantage?" Here the answer is internal, if art. 50 is not invoked and there are not ongoing negotiations (because the EU won't agree without art. 50), people at home will begin claiming that Theresa May is not complying with the Brexit referendum and she will lose her support.