Last update: 15:10 | 26/06/2018
The Financial Conduct Authority (FCA), says it will now work with the industry to direct people to specialist cover.
One trade body said it was "absurd" that such a large group of people were unable to travel.
It is hoped that the action by the FCA will help 15 million people with long-standing health conditions.
The regulator added that this group was expected to rise to 18 million in the next decade.
In a report, focusing particularly on those who have had cancer treatment, it said that many of these people had become marginalised by the insurance sector.
A lack of information about alternative cover after people had been given expensive quotes or refused cover owing to their condition, or past condition
A lack of understanding among insurance companies and their customers about what risks are considered when setting prices
Unclear pricing of premiums
This led many people to feel that they were uninsurable, particularly after failing to find travel insurance via a price comparison website, and despite the fact there are a host of specialist firms ready to cover them.
Melissa Collett, professional standards director at the Chartered Insurance Institute, said: "One in three people living in the UK are likely to get cancer at some point in their lives and it is absurd that this large group are prevented from travelling because they cannot get insurance or worse, forced to risk travelling without it.
"Many people living with cancer and those in remission live healthy and full lives and we should be doing all we can to support them in this."
Some of those who faced difficulties found frontline insurance staff had little understanding of health conditions.
One 58-year-old woman said she had undergone surgery to remove a 2mm cancerous "freckle" more than six years ago. Regular check-ups followed and she was declared cancer-free in December 2015, and yet even since then she had struggled to get insurance.
Another had faced premiums of hundreds of pounds after receiving treatment for "low-grade bladder cancer".
"I do not understand why I am charged very high premiums every time I travel abroad as my cancer history does not necessitate any medication or treatment and has no impact on my daily life," the respondent explained to the FCA.
Macmillan Cancer Support said it had received 900 calls since January about travel insurance and suggested that the plans from the FCA needed to go further.
"Improved signposting will only benefit people with cancer if, at the end of it, there is fair and affordable cover available. As it stands, this is rarely the case," the charity's executive director of policy, Fran Woodard, said.
"No two cancer experiences are the same and if travel insurers want to meet the need for people with cancer, they must update their oversimplified medical screening to reflect this."
The Association of British Insurers (ABI) said it was vital that people were clear about pre-existing medical conditions as medical costs could reach tens of thousands of pounds for complicated treatments in countries outside Europe, so insurers needed to allow for that.
However, Raluca Boroianu-Omura, head of conduct regulation at the ABI, said that the industry was open to finding new ways of helping people find appropriate cover, in addition to work it had already done with cancer charities.
David Sparkes, head of compliance at the British Insurance Brokers' Association, said specialist insurers could ask precise questions about a customer's health condition to judge levels of risk, which meant that cover did not need to be more expensive.
He said it was important that signposting to these firms was available to people with various health conditions, not only cancer.