Sick note after isolation

[stressingmum]

I'm having trouble getting a sick note after testing positive for Covid.
The history is I tested positive 14th Jan was given the isolation note from NHS track and trace after the 10 days I was still unwell and still am now I've got fatigue and headaches which mean I'm still napping in the day and when a headache starts it is generally leading into a migraine.
As it's now past the original 10 days my employer phoned and asked for a sick note I can't work from home and the drive is about 30 minutes I don't feel it would be safe for me too go in. So I phoned the doctors and was told to do a isolation extension online which I've done my employer is saying this is not good enough, phoned the doctors again and spoke to a GP this time who advised me they have sought advice on the subject and they have been told they do not need to issue them as it would be a drain on there resources the typical recovery from Covid is 4 weeks and the isolation extension should cover this period and employers need to be understanding. I might add I've never taken any time off sick so it's not like this is something I do often.
Just wondered if anyone else has encountered anything similar? If you look on the NHS website it clearly states do not call your doctor for Covid related issues until 4 weeks is up including for sick notes.

I’m sorry you are experiencing this hassle when you are still feeling unwell.

I suggest you email your employer a link to the page you mentioned on the NHS website, and also tell them what the doctor told you.

I wonder if this varies from surgery to surgery? It does seem unfair for you, especially when you are still unwell.
A colleague has just been signed off by her GP for a further month, with long covid. She tested positive around the same time as you.
I think all you can do is what the above poster suggests - send a link to your employer, and tell them what your GP said.