NHS data shows 37,644 people had received both jabs by May 9 – 23% of those aged 16 and over, based on the latest population estimates from the Office for National Statistics.
Of those to have received both jabs, 32,644 were aged 40 and over – 37% of the age group.
It means 5,000 people aged between 16 to 39 have received both doses.
Across England, a third of people aged 16 and over have received their second vaccine dose.
The NHS vaccine data also reveals variation in coverage for residents who had received at least one dose between different areas across Luton.
Across Luton, 55% of those aged 16 and over have had one jab.
Areas with the highest coverage:
1) Bramingham, with 73.7% of people aged 16 and over given their first dose
2) Warden Hill, 72.6%
3) Stopsley North, 72%
Areas with the lowest coverage:
1) Central Luton & Park Town, 31.9%
2) New Town, 35.3%
3) Dallow Road, 39.6%
Across England, 15 million people had received a second dose of the jab by May 9 – 33% of the population aged over 16 and over.
That includes 13.3 million people aged 40 and over – 47% of the age group.
In total, 29.4 million people had received at least one dose of a vaccine by the same date, covering 65% of people over 16.
Despite the success of the rollout, some staff at care homes in Luton have not been vaccinated.
The figures show 688 out of 1094 eligible staff, including agency workers, at older adult care homes had received a first dose by May 9 – meaning 37% have not had a jab.
The Government is currently in consultation over plans to make the jab mandatory for staff over concerns for residents.