The UK will give both parts of the Oxford and Pfizer vaccines 12 weeks apart, having initially planned to leave 21 days between the Pfizer jabs.
The British Medical Association said cancelling patients booked in for their second doses was "grossly unfair".
But the chief medical officers said getting more people vaccinated with the first jab "is much more preferable".
Pfizer has said it has tested the vaccine's efficacy only when the two vaccines were given up to 21 days apart.
But the chief medical officers said the "great majority" of initial protection came from the first jab.
The decision to delay the second vaccine shots, made on the recommendation of the UK’s joint committee on vaccinations and immunisation (JCVI), has sparked widespread concern among experts, healthcare professionals and the vaccine producers themselves.
More than 180,000 people have signed an online petition at change.org in protest of the decision.
Dr Julian Povey, a local GP and chair of Shropshire and Telford & Wrekin Clinical Commissioning Groups, has said patients in the county, who are eligible for the vaccine, will now be notified of changes to their appointments.
He said: "In light of the JCVI advice in dose prioritisation, delaying the second Pfizer jab to 12 weeks, Shropshire, Telford & Wrekin's Sustainability and Transformation Partnership will be contacting patients in Shropshire, Telford & Wrekin, with second appointments booked in the next few days into next week to rearrange and give new dates.
"This call will be from a local call centre not from your GP practice, they will give you details including your GP practice and then confirm a new date 11-12 weeks after your first vaccination.
"This decision is clearly not universally supported but we are in extraordinary times, with rising pressure on health services, and rapid decisions need to be taken and then enacted."
Debbie Oliver, an advanced nurse practitioner in Lancashire, started the change.org petition just a few days ago and it is being shared widely across social media, in a sign of public concern on the issue.
She said: "We want the UK Government; Matt Hancock & NHS England to vaccinate frontline workers/vulnerable public with the evidence based dosing regime as per vaccine schedule not one they decide is better.
“We want 94 per cent from Pfizer vaccine not 52 per cent from one dose for three weeks only to be gambling with people's lives after week three in the misguided hope half protection is better than none.
“UK Government you are letting down all those who put their lives on the line (and those who lost lives).
"Do the right things and put back the correct dosing regime as per study data."
The petition can be signed at www.change.org/p/uk-parliament-2nd-covid-vaccine-should-be-21-28-days-not-12-weeks-challenge-the-u-k-government