Should the United Kingdom remain a member of the European Union or leave the European Union?
BMG, online :
Remain 45% (-4)
Leave 55% (+4)
BMG, telephone :
Both polls were fully conducted prior to the murder of Jo Cox, and indeed the fieldwork started as long ago as the 10th. So in a sense this is historical data that can only contribute to our understanding of the state of play prior to the tragedy. The online figures are entirely as expected, with the same sort of swing to Leave detected recently by ICM and YouGov. More surprising is the decent lead for Remain in the phone poll, but it's hard to draw any conclusions about the trend from that, because there are no baseline figures to work from - this is BMG's first phone poll of the campaign.
The big question is whether BMG followed the same practice as ICM did with their own recent simultaneous online and phone polls, by using exactly the same methodology (apart from data collection method, obviously) for both polls. If they did, this is a direct contradiction of ICM's finding (that was successfully replicated after a fortnight had passed) that the divergence between phone and online polls has closed.
Even so, BMG are not one of the big names in political telephone polling, so although reputation is no guarantee of accuracy, I would be inclined to give more weight to the ICM and Ipsos-Mori phone polls - conducted at roughly the same time - putting Leave ahead.
We still await the first credible poll to be conducted since the murder. USA Today are reporting "poll data" from yesterday (ie. the 17th) supposedly showing a swing towards Leave, but from the limited information available, it doesn't sound like a proper representative poll to me.