I think the writer uses the term 'upstart' to characterize how s/he thinks Mr. Brown feels about Mr. Cameron.
One person's upstart is another person's energetic newcomer. The word upstart is used to describe a person, new on the scene, who exerts (or tries to exert) influence in a situation. For example, if A has been working at XYZ Corporation for ten years, and B, who has only been there for six months, starts to exert control and effect changes that threaten A, A may call B 'an upstart'. On the other hand, people less threatened by B may call him/her 'an innovator' or 'just what the company needed'.
The connotation of the word upstart for me is that it's a word used by stodgy people who are threatened by anything new.
All best wishes,