The scheme's eligibility criteria in England were expanded in August to include people with conditions such as Parkinson's, dementia and epilepsy.
This was the biggest change to blue badges since they were introduced in 1970.
In the first three months under the amended rules, 12,299 new badges - around 130 a day - were granted to people who cannot walk as part of a journey without "considerable psychological distress" or the risk of "serious harm".
Depending on the location, the permits often enable holders to park free of charge in pay-and-display bays and for up to three hours on yellow lines, helping people access shops and services by allowing them to park closer to their destinations.
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However, the roll out was not smooth in Sheffield, where in October, the Local Government and Social Care Ombudsman revealed at least 25 disabled people had been wrongly denied a face-to-face assessments for their blue badge, leaving potentially vulnerable people without access to their high streets.
Sheffield Council has agreed to contact those who missed out on assessments.
Transport Secretary Grant Shapps said people with hidden conditions endure the "psychological worry that others may not recognise them as disabled".
He went on: "I'm proud that our reform is already changing thousands of people's lives, allowing those in need to carry on their daily lives with more confidence and helping combat loneliness and isolation."
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Samantha Tomlin, whose son Henry has autism and is a new recipient of a blue badge, said: "When my son was younger sometimes I didn't go out because I just couldn't face trying to find a safe place to park near the shop or doctors.
"Having the blue badge just makes you feel slightly less anxious about the situation and feel your child is safer.
"It will make a huge difference to parents going through the early years and those with older children and adults that suffer with all the challenges autism brings."
DfT figures published earlier this month showed prosecutions of motorists misusing blue badges reached 1,432 in the year ending on March 31, up nearly a fifth compared with the previous 12 months.
Nearly all the cases involved someone using another person's badge.