The lead story on BBC News this morning is that "the BBC has learned" (i.e. doubtless meaning that it's been told all about it by the same pro-EU campaigners who star in the article itself!) that various lawyers and a "think tank" are considering legal challenges to the government over the single market:
The article, after outlining the arguments of the lawyers, then refers to British Influence:
"Think tank" is one way of putting it. It doesn't appear to be the correct way though. "Pressure group" seems more accurate. Wikipedia says this of the organisation:
You get none of that background in the BBC article. Even the website of the organisation jokingly calls itself a "re-think tank" (i.e. a campaign group rather than a proper think tank). The BBC is making them sound like 'experts'.