I hear you, OP - and I completely agree with you. It's the fact that they expect you to do part of your work (booting up a computer, logging in etc.) unpaid and then claim that only your actual customer-facing/hearing time is actual work - the rest is so petty as not to be worth paying, yet is somehow nevertheless important enough for them to insist on it! They value your time only insofar as it can make them money, but otherwise, your time is considered worthless.
Why is it 'only a few minutes' to you but never the same to the employer? And then others who are taken advantage even more of than you are come on and tell you that you should be grateful!!
Conversely if you sat down at your desk at 9am then turned on your computer and logged in you would be overpaid by several hundred pounds a year.
Not at all. This would only be true if OP did not need to do any logging on in order to do her job, yet somehow still insisted on spending two minutes each day in her unrelated unusual personal 'hobby' of 'unnecessarily turning on a random computer' before beginning work, all on the company's time.
If I were going to a concert (for my own enjoyment) that started at 8pm, I would expect to arrive there at least 5 minutes early - giving up 5 minutes of MY time, to be prepared to do something that I want to do - to be ready for when the main thing started. Similarly, if I were attending a meeting that my employer insisted I be present at, and they (wisely) expected me to be there 5 minutes early, that extra 5 minutes would be part of the whole task and thus payable by the person paying for the whole task.
You wouldn't pay a painter by the hour to decorate your living room and then only expect to pay him for the time he's actually slapping paint on the wall - telling him that you expect him to prepare the surfaces and materials, protect the carpets, move furniture etc. and then tidy away afterwards, all in his own, unpaid time - just because you don't personally see a direct tangible benefit to the time he takes doing those crucial parts of the job for which you're paying him.