But Stafford was one of only 23 local authority areas to see a rise in first jabs, while the number delivered across England was the lowest recorded in the proceeding five weeks.
NHS England warned last month that supply issues would mean priority for the jabs would be given to those in the high-risk groups and for second doses.
Data from the health body shows that 1,257 first doses of the vaccine were administered in Stafford in the week to April 11 – 227 more than the week before. Across the five weeks to April 11, though, the highest number of weekly vaccines delivered was 6,729, during the week to March 14.
Meanwhile, 1,597 first doses were administered in Sandwell that week – 1,918 fewer than the previous week; 1,544 in Dudley – 2,727 less than the previous week; and 1,553 in Wolverhampton – 778 fewer than the week before.
And in Staffordshire, 745 first doses were administered in South Staffordshire in that week – 1,173 fewer than the previous week; and 875 were administered in Cannock Chase – 806 fewer than the week before.
In all areas bar Stafford, the figures were the lowest than the proceeding five weeks.
Across the Black Country and West Birmingham fewer doses of the vaccine were expected during April – but additional vaccine supply was secured to ensure that those due their second dose and those everyone aged 45 and over and those eligible in cohorts one to nine can get a vaccine.
Sally Roberts, senior responsible officer for the vaccine programme, said: "We are pleased everyone aged 45 and over has been invited to get their Covid-19 vaccine.
“We want to ensure everyone in an eligible group has had the chance to get protected, especially those who are clinically vulnerable and most at risk of serious illness.
“We continue to see that some people are not taking up the offer of a vaccine, but no one will be left behind, the vaccine is safe and effective and people should go and get it when asked to do so.
“If you have already been offered a jab but have not taken it up it is not too late. I would urge anyone with underlying health conditions, carers, health and social care and care home staff who have not yet been vaccinated against Covid-19 to please come forward and we will get you booked in”
Across England, 355,000 first doses of the Covid-19 vaccine were administered in the week to April 11 – the lowest number in five weeks and 47 per cent fewer than the previous week.
But the number of people receiving a second dose of the jab increased by 608,000, to 2.1 million people. Numbers for second doses are not available locally.
A delay in deliveries from India and the need to retest a batch of 1.7 million doses is behind the issues with vaccine supply in April.
Local health leaders were told to focus efforts on the top priority groups in a letter signed by Dr Nikita Kanani, medical director for primary care for the NHS in England, and Emily Lawson, chief commercial officer.
But last week, "phase 2" of the vaccination programme was announced – with the roll-out being widened to include those over the age of 45.
A Department of Health and Social Care spokesman said: “Our vaccination programme continues to make phenomenal progress – with over 40 million vaccines administered so far across the UK.
"We have hit our target to offer a vaccine to everyone in phase one of the vaccination programme and we are on track to offer a jab to all adults by the end of July.”