That's rather a sweeping generalisation, and it hasn't always been the case. There's been no shortage of times in the past when other EU countries, particularly France during the Blair years, were complaining that the UK had too much influence rather than too little.
It's impossible to quantify, of course, not least because about 90% of Council of Ministers decisions are arrived at by consensus without a vote. But you can point to the various EU measures which originated in existing UK national legislation or which were promoted by British Commissioners (in areas such as farm animal health, industrial health and safety etc.), and British Commissioners have occupied some of the most influential posts in the Commission (Mandelson Trade, Patten External Relations, Jenkins and Kinnock President and Vice-President etc.)
It's certainly true than in recent years on the occasions when there has been a vote in the CoM, the UK has been on the losing side more often than any other member state. But that was very different before 2009 - which was again the period when there were those complaints about excessive British influence...
Yes: that has always been a popular lie out of the pro-EU left; any time the UK asserts its sovereignty and does not submit to regulations that are too draconian (within the left-wing scope that the EU wishes to project), they are suddenly wielding too great of influence and need to be taken down a peg or several. France with its affinity for Germany over the decades shows itself particularly mendacious here.
That's rather a sweeping generalisation, and it hasn't always been the case. There's been no shortage of times in the past when other EU countries, particularly France during the Blair years, were complaining that the UK had too much influence rather than too little.