Three-quarters of patients were investigated and referred by GPs to specialists within a month of their first presentation with symptoms.
But the RCGP report, which covered one in seven practices in England, also found nearly one in 10 patients with cancer waited two months or more before being referred to a specialist.
GPs at practices involved in the study blamed poor access to investigational tests and scans for delays diagnosing some cancers.
RCGP chairwoman Dr Clare Gerada said the report showed general practice does a 'very good job' of identifying and referring patients who have cancer, but that more could be done.
Patients faced hugely differing waits between initial presentation with symptoms and referral depending on their symptoms.
Around one in six patients with stomach, gall bladder or bone marrow cancer wait two months or more.
In comparison, 72.2% of patients with breast cancer were referred after one visit to their GP, and referral occurred within two weeks for more than eight in 10 patients.
Project lead and GP Professor Greg Rubin of Durham University said clinical commissioning groups must ensure access to diagnostics remains a priority during the 'considerable pressure' faced by the NHS at present.
The report is the largest study yet into the primary care pathway from presentation to cancer diagnosis and involved one in seven practices in England.
Concerns had been raised about the number of times patients consult with symptoms of cancer before being referred for specialist assessment.
The RCGP, working with the national cancer networks and the DoH's cancer teams, examined data collected on 18,879 patients with cancer from 1,170 practices in England.
It found that 73.2% of all patients had been referred to a specialist after just one or two consultations. About three-quarters of patients were referred within one month of first presentation with symptoms.
The number of consultations required before referral varied between cancer types. The report found that 77.3% of patients with breast cancer symptoms consulted just once or twice before they were referred, compared with 57.2% of pancreatic cancers.
Some cancers took much longer to be investigated, with one in seven cases of myeloma taking five or more consultations before a referral was made.Experts said these variations may reflect difficulties detecting and diagnosing some cancers with non-specific symptoms in primary care.
Dr Gerada said: 'While there are groups of patients where we do, for various reasons, have difficulty in making a rapid diagnosis, we must be proud that the majority are being identified and put into secondary care quickly. At the same time, we must always be looking at how we can improve.'
Dr Chris Carrigan, head of the National Cancer Intelligence Network, which co-produced the report, said: 'Collecting and evaluating data on how quickly cancer patients are sent for referral by their GP is crucial to equip us with the knowledge to improve early detection of the disease.'