Cockman's mastership at University College was a contested one, with William Dennison, who also served as Master between 1722–29. There were two disputed elections held in 1722. Cockman appealed to the Crown and was declared Master of University College in 1729. The success of Thomas Cockman's appeal involved accepting that King Alfred had founded the College. This myth originated from the late 1380s but it was widely believed by Cockman's time. The ruling at the court hearing meant that the Visitor of University College, who is responsible for resolving such disputes, should be the Crown rather than the University.
In 2008, University College acquired a painting including Thomas Cockman. The painting had remained in Thomas Cockman's family, but was auctioned at Sothebys. The picture is presumed to be a celebration of the success of Cockman's appeal to the Crown to be declared Master of University College in 1729.