A couple in need of dental care say they had to pull out their own teeth because no NHS dentist will treat them.
A BBC News analysis of 2,500 dental practices on the NHS Choices website found half were not accepting new adult NHS patients, while two-fifths were not accepting new child NHS patients.
The British Dental Association (BDA) said the figures reflected an "emerging crisis" in dental care in England.
NHS England said 95% of people seeking an appointment could get one.
The NHS carried out 39 million dental treatments in England last year, but Rebecca Brearey and Nick Oldroyd, who live in Dewsbury, West Yorkshire, said no local NHS dentists would treat them.
"We've been trying for four years but no dentist will take us on. Every time I go, I get told there's a two-year waiting list for NHS patients," said Ms Brearey.
"It's got so bad that after taking a combination of paracetamol and alcohol I ripped my half-rotten teeth out.
"The state of my teeth has made me depressed and I've literally begged to be taken on by an NHS dentist, but every time I've been turned away."
Mr Oldroyd said: "I was sat there for days in agony with a tooth which was doing my head in and stopping me from sleeping.
"I was drinking to just try and just numb the pain so one night I just pulled it out.
"The tops of my teeth are gone. I'm on benefits and trying to get a job, and when someone sees my teeth they just think I'm another waster.
"I do believe if I could get some dental care I might be able to begin turning my life around."
Nazreen Akhtar, from Bradford, said it had taken her five years to find a dentist in the city who would accept both of her children, Shaban and Muhammad.
"My son Muhammad has been in a lot of pain, he's had adult teeth growing over the tops of his milk teeth," said Mrs Akhtar.
"Me and my husband don't have a car so we can't travel to other cities to get care.
"I do feel let down by the NHS as we should be able to see a local dentist."
BBC News has conducted a data analysis of more than 7,000 dental practices in England that are listed on the NHS Choices website.
Just over 2,500 of these practices had information about whether they were currently accepting new NHS patients.
Of those practices displaying information about new NHS patients, 48% were not accepting new adult patients, while 40% were not accepting new child patients.
Who gets free dental care on the NHS?
Unlike receiving treatment from a GP or a hospital, most people have to pay a contribution towards their NHS dental care.
Dental charges for adults were introduced by the NHS in 1951.
Patients in England get free dental care if they are under 18, under 19 and in full-time education, or are pregnant or have given birth in the past 12 months. Those receiving certain types of benefits are also exempt.
The latest NHS England annual report shows patient charges generated £783m for the NHS in 2016-17.
The number of dentists doing NHS work has increased by 20% over the past decade, but dentists who no longer treat NHS patients say the system is chronically underfunded.
"The vast majority of dentists want to support the NHS, but we're not miracle workers and a bankrupt dentist is no good to anyone," said Dr Tony Kilcoyne, who runs a private dental practice in Keighley, West Yorkshire.
"The vast majority of dentists are self-employed so the government doesn't pay our staff or our overheads like a hospital.
"If the system is funded at about half the level that it needs to be, then we can't treat everyone."
More than £3bn a year is spent each year on providing NHS dental care, according to Public Health England, representing about 3% of the total NHS budget in England.
"There is an emerging crisis with more and more dentists not accepting NHS patients," said Henrik Overgaard-Nielsen, chair of general dental practice at the BDA.
"The government has only commissioned enough dentistry to treat about half the adult population and this is an absolute disgrace."
An NHS England spokesperson said: "The latest NHS patient survey found that 95% of people seeking a dental appointment were able to get one, and the overall number of dentists offering NHS care is 3,800 higher than a decade ago."
A Department of Health spokesperson said: "Improving oral health is a key priority for this government, and in the last two years more than 22.2 million adults were seen by a dentist.
"We expect NHS England to ensure there are sufficient dental services to meet the needs of the local population."