Hannah Gray, who is on maternity leave from Look North, gave birth to Summer Elizabeth Gray on Saturday, May 22.
Yesterday (Tuesday) the new mum went for her Covid jab, but said she was left "absolutely appalled" after being told she would not be able to get to the front of the queue.
Posting a video on Twitter, she said: "So I've just had a massive meltdown as I've come to get my Covid jab. The queue is an hour long and they won't let me jump the queue.
"So a breastfeeding woman who has left the house for the first time to come and have her jab has to go all the way to the back of this massively long queue.
"And even though my baby's hungry and I need to be back to feed her in the car, I can't queue up - I have to just wait at the back, and it's baking hot. So I'm really not impressed.
"Also I was told to just sit and wait in the car and have my husband stand in the queue but it's 25 degrees in the car. Am I going to keep my baby in a hot car and breastfeed her? I think it's absolutely appalling."
In a tweet she added: "Was really excited to come and get vaccinated today but I had to leave. I couldn’t stand in the heat with 10 day old Summer for over an hour waiting."
"The security men told us to put our newborn baby in the car when I complained about sun! It’s 20+ degrees and she shouldn’t be in heat for that long or in a car seat for that long (including travel time). Why isn’t there a priority system?"
Hannah said that today (Tuesday) she had received an apology from the head of the vaccination centre.
She told the YEP: "He called me at 9am and apologised and said the security guards made the wrong call.
"There was a breastfeeding room indoors and they should have gone and got a senior nurse in charge to assess my situation.
"He listened to my story, agreed that my baby was put at risk from too long in the sun, too long in the car seat, and it was not a sensible solution for them to suggest putting her in a hot car with my husband as he can’t breast feed her and she’s lost a lot of weight since birth so as soon as she needs a feed I’m supposed to feed her.
"They’re booking me in for next week and say they’ll take care of me and make sure I don’t have such a long wait next time."
Gareth Dalby, Centre Manager at NHS Vaccination Centre at Elland Road said: “We’re really sorry Hannah had this experience.
"It was a mistake on our part and we are pleased to see Hannah is rebooking her Covid vaccination with us soon.
"We can make provision for breastfeeding mothers on site and we will make sure all our staff at Elland Road are aware of this in future.”
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