Text messages are now going out to 40 and 41-year-olds in the county, allowing them to arrange a jab through the national booking service.
Health bosses in Shropshire have also issued a plea for people to make sure they return for their second jabs, saying it is crucial to get the strongest possible protection against the virus.
Latest NHS England figures, published yesterday, show that 384,432 doses of the vaccine had been given across Shropshire, Telford and Wrekin by the end of Sunday.
Around two-thirds of those aged 45-49 in the county have now received their first jab, while almost 108,000 people had received their second dose of the vaccine at the end of last week.
Nearly three quarters of a million appointments were made on Monday and Tuesday as the NHS began inviting 44-year olds followed by people aged 42 and 43 by text.
Those aged 42 to 44 have already been text this week, meaning in total another 2.5 million more people have been invited for their jab.
Since the vaccination rollout began in December, more than 28 million people have been protected with at least one dose in England – nearly two thirds of the adult population.
NHS staff have fully vaccinated more than 11 million people, with second doses remaining a priority.
NHS England chief executive Sir Simon Stevens said: "With nine tenths of people aged 45 and over having been jabbed, nearly three quarters of a million new appointments were made in just two days as our booking service opened to people aged 42 to 44.
"With second doses also proceeding apace, we're now ready to invite all those aged 40 and over to join the most successful vaccination drive in health service history."
NHS medical director, Professor Stephen Powis, added: “The rapid rollout of the NHS vaccination programme, the swiftest in Europe, 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 for your jab, please follow the instructions provided and book – it is simple, effective and provides vital protection against the virus.”
The NHS is vaccinating in line with guidance from the Joint Committee on Vaccination and Immunisation as supply allows.
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 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, call 119 or go to nhs.uk/covidvaccine