CPT is a known traffic magnet. Within the TMA it is not unusual to have aircraft at or around CPT at every FL between FL70 to FL150, often more than one aircraft at each level.
Chances are that most of the headings are from TMA controllers, that's the nature of the beast due to the airspace. As you get higher, you tend to be on actual airways and therefore more likely to be established on a single heading.
However 14 turns is excessive, unless something out of the ordinary is happening. On a CPT departure on easterlies you could reasonably expect 1 or 2 headings from Director and maybe another two on the TMA freq (34.12). However depending what is going on you could have more.
Heading instructions
220, 225, 240, 245, 260, 275
one after the other as you say seems very unlikely - I assume that was an easterly departure? All of those headings (if a true recollection of events) would have most likely been on the EGLL Dir frequency - very excessive and poor use of headings
if the figures are true.