The Screening for Heart Attack Prevention and Education (SHAPE) guideline said screening was needed to implement preventive strategies.
But Dr Rubin Minhas, GP and CHD lead for Medway PCT in Kent, said that this approach would be too expensive for the UK and that it was better to focus resources on developing an optimum risk assessment tool.
'A two-stage model using risk factors with scanning would be ideal,' he said. 'But resources and cost implications are a barrier to that at the moment.'
He added that the Framingham tool was 'irrelevant to the UK population and out of date'.
He said that the London Lifestyle and Population (Lollipop) study, which is being coordinated by researchers from Imperial College London, contained four times as many people as Framingham, and could form the basis of a UK risk score.
Tools such as the Ethrisk calculator have been developed to make the Framingham risk score more appropriate for patients from ethnic minorities.
But Dr Minhas said these were just stepping stones.
RCGP vice chairman Dr Graham Archard said: 'Framingham does not represent the UK population. We need an alternative.'
But North Yorkshire GP Dr Terry McCormack, chairman of the Primary Care Cardiovascular Society, said that developing yet more screening tools would only lead to confusion: 'People need to look to standardised cardiovascular risk tables as published by the Joint Societies.'