Hello and welcome to SAYNOTO0870.COM.
Firstly, it's highly doubtful that anyone who uses this site
knows the number; as in such circumstances they should submit it for listing in our database.
However, it is not beyond reason that we may be able to sleuth it.
The website is
www.ainsdale-mc.co.uk and it gives the fax number as 01704 573875. Googling that returns pages giving the voice telephone number as 01704 574137. I rather suspect you are going to tell me that that is the old number before they got the premium one.
What this does tell us is that the current fax number has been in use since before they got the phone system/service, of which the 0844 number is a part. It is therefore unlikely that the 01704 fax is a clue to the numbers they operate.
Do you know of other information such as other numbers that are known for the surgery? For example, are district nurses/health visitors based there and if so, what number do they give?
I will have another look later when I get a bit more time; see what I can come up with.