"Doctor would not see me after being 5 minutes late"

Terrible terrible service, it was raining and I tried the machine first to sign in, didn’t work. Then reception, that took few minutes and staff member said doctor would not see me today cos I am late. What?!. It was less than 5 minutes late and I was refused to be seen? I hardly visit nhs but they didn't seem to care. On the other hand it’s always ok for them to let us wait for nearly 30min nearly every single time after you have signed in for appointment? I feel it’s not right and it’s not acceptable at all. It made me sick to my stomach.