Dudley North MP Marco Longhi said Britain's departure from the EU had helped the country to "lead the world" in the fight against coronavirus.
According to the latest figures the UK has delivered the vaccine to 4.6m people, including 97, 310 doses in the Black Country and West Birmingham up to January 17.
Only China and the USA have administered more doses than the UK.
Meanwhile the EU has been condemned for the slow roll out of its vaccine programme, with some member states saying they were late to receive doses.
Conservative MP Mr Longhi, who visited the vaccination hub at Northway Medical Centre in Sedgley this week, said the UK's vaccination programme had "got off to a fantastic start thanks to the hard work of all of those involved".
He added: “It’s great to see that so many people in my area have received the vaccine as we lead the world in our fight back against coronavirus.
"Brexit really has helped save lives as the UK was free to implement our own vaccine programme."
Some pharmacies will also start delivery, including Pharmacy Xpress in Dudley.
Mike Wood, Conservative MP for Dudley South, said the number of vaccinations across the region so far was "an amazing achievement" that would "help to save lives in our community".
He added: "When I saw the vaccination centre in Kingswinford I saw the incredible work being done by doctors, nurses, pharmacists, staff and volunteers to make it all run smoothly, and how overjoyed patients were as they came out having been vaccinated.
"A massive thank you to everybody who has made this happen, and who are working to make sure we can protect even more people even more quickly as more vaccines become available."
Health chiefs in Dudley say they hope to have all care home residents in the borough vaccinated by the end of next week.