Blinking heck I missed the vet comment!
Here´s the crux of the matter, what patients see in the waiting area´s etc and what is actually happening "behind the scenes" is if often vastly different.
A consultant may have had to take a phone call from someone eg. another consultant asking for his opinion, a follow up call, his secretary asking if x,y,z patient can be booked in as an emergency. He maybe the duty consultant that day and has been called to a ward, A and E, etc. etc. This could happen before, after or during clinic.
Theatres and operations can be delayed due to emergencies, specific staff being needed in an emergency eg. anaesthetists, surgeon etc.
The recovery rooms can become clogged due to several post op patients having issues,
Beds are a finite resource in most hospitals, we can not produce them out a hat, it is often a juggling act, of waiting for discharges, putting on a less than perfect ward holding patients in resus or A and E, transferring, this is a difficult job and the people that do it try there level best at all times to get patients into suitable wards, care levels but some patients will have to wait.
The theatres might be needed for an emergency, none routine, more serious condition which means that routine surgery falls to the bottom of the list.
A patient might take longer in his or hers appointment due to mobility issues, comprehension problems, fear, phobia, complicated medical issues, the need to prescribe, refer, confer and 1001 other reasons.
The computer system may go wrong meaning that notes etc take much more time to access for example current medication, referrals etc. this means the whole process becomes very long and tiresome for all concerned.
Some clinics are more at risk of over running than others, simply due to the nature of the medical situations they deal with.
Some doctors actually encourage patients to take there time and bring up anything they are worried about - have to read back in the notes and check things etc. But the great thing is that whilst you have sat and waited that doctor will deal with you in the same way.
Sometimes doctors are ill etc. and that means either cancel x number of patients or try and get everyone scene.
Sometimes doctors are late getting to work (does happen), have to go to the loo, grab a drink etc.
There are so many reasons that clinics run over time that it is almost a miracle when the run on time. Trust me all the clinic staff would much rather run on time that be late. Also sometimes the admin staff just DON¨T KNOW, yes if a doctor is off they should know this and be able to advise accordingly, but often they know nothing more than the clinic is running late and there are x number of patients in front of you waiting to be seen.
Short of having a team of doctors, nurses, aux staff, spare wards going unused, spare treatment rooms. etc. etc. etc. sat in hospital just in case X,y,z happens which the funding is simply not available for. There will be delays and there is nothing really that can be done about them either by the hospital / medical staff or by the patients. They are just a fact of the NHS, unpleasant yes but undeniable.
The fact is complaining vigorously to the front of line staff is not going to change funding and policy for that you need your MP and no the NHS is not free it is FREE at the point of use, and yes some people will pay in more than they use (same as private insurance), and yes everyone is funding everyone's treatment.