A hospital told a patient she would have to wait 18 months for an MRI brain scan, before giving her a number to call for private treatment.
Ms King was told the private MRI scan would cost £983
King's College Hospital told Rachel King she could get the scan privately at the hospital in two weeks.
The hospital accepted wait times were unacceptable and said it had recently got funds to help tackle the issue.
It later revealed accident victim Ms King, 32, from Kent, would receive the scan on the NHS in September.
Ms King told the Times she was appalled when she received the original letter, saying: "It's insulting. I was distraught."
In a statement King's College Hospital said it would expand its services with the aim of getting waiting times down to 26 weeks by next March.
It added that patients identified as clinically urgent were seen sooner, and that a note given to Ms King included the phone number for private scans because she had discussed that option with her consultant.
A letter informing her of the delay included a handwritten footnote which said that "if you want to go privately" a certain telephone number could be called.
A hospital spokeswoman told the BBC News website it was not usual practice to include information on private treatment in patient letters, but it only occurred when patients asked.
Ms King suffered head injuries, a broken collarbone, five broken ribs and a broken shoulder blade after a road accident in January.
She was referred for an MRI scan after suffering dizzy spells and reduced vision.
She told the Times: "I needed reassurance that the damage isn't permanent. All I want is to know if it is going to get better."
When she called the number, which was for the hospital's own 'self pay' private clinic, she was told the scan would cost £983.
But after she received the standard letter Ms King's consultant had made an appointment for her to return in September. This would have automatically generated an appointment for her scan prior to the consultant date, said the hospital.
If Ms King had followed up the letter with a phone call she would have been told this, said the spokeswoman, or otherwise would have been informed of the date and time by letter in July or August.
'Not good enough'
Health minister Lord Warner told the paper the government wanted to ensure the NHS delivered the best possible treatment as quickly as possible.
"By 2008 no one will wait longer than 18 weeks from GP appointment to treatment.
"For the first time in the history of the NHS hidden waits for diagnostic procedures such as MRI scans will be identified and eradicated," he said.
"It would be completely unacceptable for any hospital to ignore their obligations to provide speedy access to NHS treatment and no hospital should make patients feel pressured into pursuing private treatment," he added.
Senior opposition MPs weighed in with criticisms about waiting times.
Shadow health secretary Andrew Lansley said the government talked of them coming down but people were waiting far too long for diagnostics.
"There is increased MRI capacity but not enough staff in the NHS to keep them operating longer hours," he said.
Liberal Democrat health spokesman Steve Webb added: "To have to wait 80 weeks just to get a diagnosis before you end up on the official waiting list figures is just simply not good enough."