The government is looking at introducing a new offence of causing death by dangerous cycling following concerns that there is no suitable legislation to deal with riders who are involved in incidents such as hitting pedestrians on pavements.

A transport minister has privately promised to support a bill presented to the House of Commons by Andrea Leadsom, the Conservative MP for South Northamptonshire, who is campaigning on behalf of a family whose teenage daughter was struck and killed by a reckless cyclist.

The move follows a significant increase in cycling in many parts of the UK over recent years and a parallel spate of alarmist media stories about "Lycra louts".

The plans have been criticised by cycling groups who argue such deaths are so rare that a new law is unnecessary, as well as a distraction from a far bigger threat to pedestrians posed by cars. In 2009, the last year for which road death statistics have been collated, no pedestrians were killed by cyclists whereas 426 died in collisions with motor vehicles.

Cyclists can be fined for dangerous or careless cycling but more serious offences can only be dealt with under a section of the 1861 Offences Against the Person Act originally aimed at the "wanton or furious" driving of a horse-drawn carriage.

Leadsom introduced a bill to the Commons last month, using as an example Rhiannon Bennett, then 17, who was killed by a speeding cyclist in 2007. The cyclist was fined £2,200 after prosecutors decided that dangerous cycling was the only appropriate charge.

While such MP-sponsored bills rarely get beyond a first reading, the road safety minister, Mike Penning, has promised the Bennetts his support. "My department will consider the merits of the proposed Dangerous and Reckless Cycling Bill in consultation with the Ministry of Justice."

Mark Wardrop, a solicitor who has been working with family, said: "He met us afterwards in the lobby and said to the effect of: we agree with your arguments, and we're in the process of updating a lot of road traffic laws to bring them up to date. We would look at trying to tag this on to another bill if possible."

Leadsom, a regular cyclist, insists she only wants to clear up a legal anomaly and is not seeking to vilify fellow riders.

But the national cycling group, the CTC, argues this is unnecessary given that courts have used the 1861 act in the last decade to jail two cyclists who killed pedestrians, while drivers who kill cyclists routinely receive non-custodial sentences.

"If the Department for Transport really wants to consider this as a serious proposal, then they need to consider the use of all road traffic offences," said Chris Peck, the CTC's policy co-ordinator. "Currently, only around 25% of road deaths are prosecuted using causing death by careless or dangerous, or causing death while under the influence of drugs or alcohol. We have recorded dozens of cases where the deaths of vulnerable users, including many cyclists, are simply never prosecuted."

Jorren Knibbe, a barrister who writes a blog on cycling law, argued that while Leadsom's bill would "fill a gap in the law" but it would be wrong for cyclists and motorists to receive similar punishments for the offence.

He said: "The number of pedestrian casualties brought about by cyclists each year is tiny, whereas the risk posed by cars is, statistically, much greater. So greater deterrents are needed for motorists, because it's much more important for everyone's safety that motorists are made to think twice before driving dangerously or carelessly.

"More generally, it's a shame that the rare time which parliament spends talking about cycling should be taken up with this bill, when no one in recent memory has put forward any kind of positive cycling legislation. As Leadsom admitted, 'in the vast majority' of accidents involving cyclists the cyclist is the victim. It would surely be a better use of parliament's limited time to legislate for that vast majority of cases instead."