More than half of the firearms offences in England&Wales involved the use of air weapons, a substantial number of the rest are imitation weapons, and only 12 of over 8,000 recorded violent crimes involved a machine gun (http://webarchive.nationalarchives.gov.uk/20160105160709/htt... table 3.02)
A study by the police of the gun crime market (http://webarchive.nationalarchives.gov.uk/20110218135832/htt...) concluded that automatic weapons were mostly used in gang warfare and as a status symbol; they're more expensive and the study noted that ammunition for all weapons was in short supply, which would make a bullet-hungry gun less attractive for other criminal usage (which is mainly to threaten).
With an imitation gun going for £20 and an automatic costing £1000, why would you choose the real gun to commit a robbery?
edit: I changed 'weaker' to 'softer', because it's a stronger claim, it's likely to stand up to scrutiny, it's almost a banality.
Say 1 guy uses a legitimate high caliber machine gun to commit some crime, is that the only crime that gets used when describing how criminals are armed in that country?