The coat of arms is for Emmanuel College in Cambridge sure enough and the EBC stands for the Emmanuel Boat Club. The misspelling of “Emmanuel” with a double ‘L’ is curious and must have been drawn/printed by someone unfamiliar with the college.
I doubt the picture was taken at Henley on the River Thames in Oxfordshire. The Henley Royal Regatta of 1910 took place in July, not May. Bengough & Chawner participated that year representing Emmanuel, but not in the pairs competition. There were and are other lesser events such as the Henley Town and Visitors' Regatta, but that traditionally takes place on the same course in August after the Royal Regatta is finished. Perhaps there were other smaller events taking place in May, but Emmanuel were pretty active on the college/university rowing circuit and there’s no particular reason to assume this achievement by Bengough & Chawner took place in Henley.
The commendation says “Burton, Pairs”, so I would think it much more likely that this refers to Burton in Staffordshire on the River Trent. Burton has held an annual Regatta since at least 1865 which is one of the finest remaining river regattas, attracting competitors from all over the country. It’s modern incarnation also takes place in July but I don’t know if that was the case in 1910 and, again, there were and are lesser events outside the main regatta dates.