take too long to have something investigated on the charity of the NHS
Not my experience. Taken instantly into hospital on Easter Saturday, seen by a consultant on Easter Sunday morning, back for various tests quite quickly. NHS verdict, as quickly as one could have expected: "there's nothing wrong with you".
But this opinion wasn't good enough for the CAA who took two years and a grand or so and several more consultants saying the same thing before they gave me my medical back.