Well here is the WSJ's opinion (citing independent studies), from the article posted above. It's behind a paywall, so I'm just posting some relevant extracts. Hope that's ok.
In Brexit Debate, U.K.’s Lack of Influence in EU is Greatly Exaggerated
Simply counting up times the U.K. was outvoted tells us nothing useful about Britain’s sway in the bloc, Simon Nixon writes
(...) The main evidence used to support these claims is a report produced last year by the euroskeptic Business for Britain campaigning organization, which found the U.K. voted against 55 pieces of EU legislation since 1996 but was outvoted each time. What's more, it said 21 of those British objections were registered since 2010 alone and the U.K. has been outvoted far more times than any other EU member.
(...) Yet the truth is that the U.K. is far from marginalized or lacking in influence.
First, it is important to note that simply counting up the number of times the U.K. was outvoted in the European Council tells us nothing useful about U.K. influence. These 55 "no" votes account for just 1.9% of all votes in the Council since 1996. (...)
Besides, votes in the Council give little insight into who comes out on top in Brussels deal-making. Much of the hard bargaining takes place long before decisions reach the Council floor; governments set out their priorities and red lines early in the process and the details are hammered out between EU ambassadors. Unpopular initiatives may be killed off before they come to the Council.
When it comes to voting, countries adopt different approaches. France, for example, rarely votes against any EU proposal: It will fight hard for its priorities in negotiations, but prefers publicly to side with the consensus rather than be seen to have been outvoted. The U.K., in contrast, is more willing to register any disagreement, reflecting domestic political pressure to be seen as "standing up to Brussels," a trend that has intensified since 2010.
Political scientists have tried to devise other ways to analyze EU decision-making to figure out which countries are influential. For example, one study asked officials from across the member states with which countries they most closely cooperated in EU rule-making. On this score, the U.K. stands out as the most influential: 20 of the 26 delegations cited U.K. officials as among their principal partners, reflecting the U.K.'s perceived success in securing its objectives.
Another study looked at how closely the outcomes of EU negotiations reflected the original policy positions of national governments; again the U.K. scored highly, coming out fourth, ahead of France and Germany. That may reflect the U.K.'s rigorous approach to EU legislation, which requires broad cross-government consultation to identify British negotiating objectives.
(...)
Indeed, one reason so many member states desperately want the U.K. to remain in the EU is because they fear the loss of British influence.