"No flexibility for blood test, unless you live..."

I was referred for a blood test by a specialist at Weybridge community hospital but because my GP is in Hersham they will only see me between 7am and 8am. They are happy to see patients with GP's in Weybridge at any time, but not referrals from their own specialists within the centre. I explained that the 7 to 8 am time was practically impossible for me to no avail and assistance.

Suppose living in Weybridge is more important than my blood test?