More than 340,000 doses have been given to people in Shropshire, Telford and Wrekin and nearly 70,000 people are now fully vaccinated.
Health bosses are also stressing it is crucial everyone goes back for their second jab, as it gives the strongest possible protection against Covid-19.
It comes after there was a change to opening hours at the county's Covid vaccination centres this month, due to national supply issues.
But the NHS has forged ahead this week with offering first doses to further patients.
Dr Jess Harvey, from Much Wenlock and Cressage Medical Practice, said the vaccination roll-out was going well, despite the national issues.
She said: "We've been focussing on doing second vaccines.
"We have had a busy few weeks. It's great that we are getting through them.
"The vaccination confidence in the younger age groups maybe lower than the older age groups so we are expecting more questions.
"It's a case of us making sure they have the information from reliable sources.
"If they have further questions they should contact their GP, rather than just not having it.
"We need to get as many people vaccinated as possible. Although hospital cases are going down, we need to minimise the virus in the population."
NHS medical director, Professor Stephen Powis said: “Just two weeks after rolling out the vaccine to those aged 45 and over, we are now ready to invite those aged 42 and 43, as the largest vaccination programme in NHS history continues at speed.
“The rapid roll-out of the NHS vaccination programme, the swiftest in Europe, hasn’t happened by accident – it is down to months of careful planning and sheer hard work by nurses, doctors and countless other staff supported by our volunteers.
“If you receive a text inviting you to book in for your jab, please follow the instructions provided – it is simple, effective and provides vital protection against the coronavirus.”
Many more patients are now due to return for their second jabs across the county.
People who booked their first appointment through the national booking service will have booked both their first and second appointments at the same time, and are being reminded they can log in at www.nhs.uk/covidvaccine to see their arrangements.
Those who called 119 will have been given details of their second appointment over the phone.
People who received their first dose in a hospital hub or through a GP service will be contacted to receive the second part of their vaccination, approximately 11 weeks following their first jab.
They do not need to contact the NHS.
However, if they are not contacted, they should call the booking line that organised their first appointment.
People who had the first part of their vaccination at a hospital site should contact the Robert Jones and Agnes Hunt Hospital and the Royal Shrewsbury Hospital booking line on 0345 678 9011.
Those whose first vaccine appointments were organised by GP practices, should call their GP practice.
For people who had appointments at Telford International Centre, Ludlow Racecourse and Shrewsbury Indoor Bowls Centre or a community pharmacy made via the national booking system, should call 119 or go to www.nhs.uk/covidvaccine
First appointments are still open to people in older age groups, those with a learning disability, people over the age of 16 living with an adult with a weakened immune system and carers.