The BBC Radio 2 DJ appeared on BBC Radio 4’s Today programme to discuss her campaigning to prioritise her younger sister, Frances, for the jab.
Frances, who has the rare Cri du Chat genetic syndrome, lives in a care home that recently suffered an outbreak of Covid-19.
Whiley said the effect of the pandemic on her sister’s mental health had been “extreme” and she had, for the first time, refused to take calls from family members.
“Oh my God, I can’t tell you how frustrating it is and how horrendous it is,” she said.
“It is the stuff of nightmares at the moment. I feel like I am living through a nightmare. All weekend it has been awful – really, really difficult. It has been hard for my parents, it has been hard for everyone in the care home, and it continues.”
Whiley pointed out the irony of her then receiving a message informing her that she was due to get her vaccine before her sister.
She said she was unsure why she had been called to have her jab, but suggested it could be because she is classed as a carer for her sister.
“I fail to understand, to be honest with you,” she said.
“Myself, my parents and the home have done everything we can to try and facilitate the vaccine coming in to the people who need it the most.
“She is in tier six but she also has quite bad diabetes, which in my understanding puts her in tier four because she has an underlying health condition, so I would have thought that she would have been vaccinated, but that hasn’t happened.”
The NHS initially targeted the top four priority groups – including those aged over 70, plus health and care staff – in its vaccination programme. Its goal is to have offered the jab to everyone in these groups by mid-February.
Whiley said she wanted to “speak up” for the people she believed are being overlooked.
“People with learning difficulties are neglected,” she said. “They haven’t got a voice, they haven’t got anybody there. Just badgering everybody saying ‘What about me? Help me out here.’”
She said she would give up her vaccine for her sister “in a heartbeat” if she could. “It just does not feel right.”
On Sunday 15 February, health secretary Matt Hancock revealed that a third of health workers have yet to be vaccinated.
Everyone in the top four groups has had a jab offer, with 15 million people receiving their first dose, the government said.
In England, the rollout has officially been expanded to those aged 65 and over and younger people in at-risk groups.
Additional reporting by Press Association