New advice recommends eating no more than 70g a day - equivalent to three rashers of bacon or two sausages.
Experts say thousands of bowel cancer deaths could be prevented every year if people kept to the new limits.
Advisers to the Department of Health in England say the restrictions would not put people at risk of iron deficiencies.
Bowel Cancer is the third most common cancer in the UK - about 36,000 people are diagnosed every year, and 16,500 die.
Eating 100 to 120g of red and processed meat a day - things like salami, ham and sausages - increases the risk of developing the condition by 20 to 30%, according to studies.
But some commentators have questioned whether reducing red meat consumption would put people at greater risk of iron deficiency; red meat is a very good source of iron.
Iron deficiency causes anaemia, which leads to tiredness and dizzy spells, can affect brain development and result in behavioural problems.
'Occasional steak'
But a report from the Scientific Advisory Committee on Nutrition says if adults cut back to 70g of red meat a day, there would not be much impact on the number of people with low iron intake.
"Red meat can be part of a healthy balanced diet," said the interim Chief Medical Officer for England, Professor Sally Davies, "but people who eat a lot should consider cutting down."
"The occasional steak or extra few slices of lamb is fine, but regularly eating a lot could increase your risk of bowel cancer."
The charity Beating Bowel Cancer welcomed the report.
"A diet high in red and processed meat may increase your risk of developing bowel cancer," said chief executive Mark Flannagan. "But the good news is that red meat can still be enjoyed in moderation."
Some experts, though, say the advice should distinguish between red and processed meat, which is thought to carry a higher bowel cancer risk.
The World Cancer Research Fund advises avoiding processed meat altogether.
"We would suggest that people following this new report's guidelines should try and make sure as little as possible of their 70g per day is processed," said Dr Rachel Thompson, deputy head of science for the fund.