In the morning about two hours before a meeting I messaged by manager to tell them I was going to a doctors appointment and I would miss the morning meeting, and asked to reschedule it (it's a small company). I ended up also missing a 2nd meeting in the afternoon. My manager was upset and said that because I missed half a day, unless I had a sick note, they would apply unpaid leave for that day.

They said that I took an unauthorised absence and after 3 strikes I would be sacked. They also said that I should have told them about the appointment earlier and because the afternoon appointment was with clients, it was important, and that they would have prevented me from going to that doctor's appointment if they knew earlier. This was more of a hospital outpatient appointment, hence why it took so long, and I could not miss it. I joined the company recently. 

I had just come back from a one week sick leave and they said that I "took a week off and then missed the first meeting of the week". They were also angry that this was the 3rd time that at short notice I could not make the meeting because of a doctor's appointment. My manager has also missed this same meeting due to their doctors appointments at short notice or being sick, so although I understand why they're upset, I'm not the only one who's done it. 

My manager then went on to say that while I was away they set a company-wide rule that if any employee doesn't fill in their timesheet by 5 pm each day, they would apply unpaid leave for that day and not only would the employee not get paid for that day or those days, it would cause problems for that employee's health insurance.

Our conversation was cordial and I was not made to feel my job was under threat. I promised to always tell them about doctors appointments well in advance.

I wanted to know what all this means for me and my job, and if their threats and actions are legal?