OK, to play Devil's Advocate for a minute...
In his response to any Unfair Dismissal proceeding that you bring,
your boss may well reply something like...
(i) No, he wasn't intimidating and bullying you.
He was managing you.
Managing an employee in a remote work arrangement
can require extra effort on the employer's part,
and extra accountability on the part of the worker. (1);
(ii) You were fundamentally dishonest about your work and circumstances.
He asked you to do a job. You lied to him about why you could not.
As such, you have abused the duty of good faith inherent in any employment relationship,
and certainly inherent in a remote working arrangement.
(iii) Your Medical Certificate is just a device to try to evade being accountable for your dishonesty.(2)
It is inherent in any employment relationship that a worker has a duty to keep their employer
reasonably informed about their ability to do the work (3)
You failed in that duty, and you lied to your employer.
The lying is still the problem.
Perhaps I am being unusually hard line pro-employer
(I am a good trade unionist in real life),
but I still don't see any legs for you to stand on.
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(1) It is settled law that an employer does not bully a worker merely by
exercising their prerogative to check and supervise their work,
and/or analyse or critique their performance.
(2) While it is likely that (like many) your employer thinks that they can
make layman second-guesses at the validity of a Medical Certificate,
they can't. Fit/unfit is all there is.
That being said, work is not like school - "a note" is not a magic bullet to get you out of something, no questions asked.
Your GP is quite within his rights (and is acting according to his own duty)
to refuse to divulge clinical detail.
If your GP says (to your employer) something like
"No. Not without a Court Order."
then that's enough.
(3) Such as when telling the employer that they are sick and unfit for work, even if not in all the clinical detail.