A 90-year-old woman died when she was hit by a scooter in September 2009, and a toddler was injured last year.
Last September, 90-year-old Lillian Macey, of Harlow, Essex, died after being hit by a scooter as she walked along a pavement in Sandown in the Isle of Wight.
When toddler Madison McNair was run over by a pensioner on a mobility scooter in Doncaster, South Yorkshire, earlier in the year, police said they could take no action because scooters were not classed as motor vehicles.
Some councils have introduced classes to improve scooter skills
The Commons committee said the increasing use of scooters meant the government needed to assess the scale of the problem.
At the moment there is little data on the numbers of people involved, or the seriousness of accidents.
Committee chairwoman Louise Ellman said mobility scooters were a "vital aid" for many people in the UK.
"We welcome the independence that these vehicles can give people to go about their daily lives," she said.
It is a balance we have to get right, because mobility scooters fulfil a very valuable and important function, helping many people to enjoy a much better quality of life
Kevin Clinton Royal Society for the Prevention of Accidents
"However, we are concerned about the many reported accidents and injuries involving the scooters.
"The government does not have adequate data on either how many mobility scooters are currently in use or on the number and type of accidents in which they might be involved."
The MPs' report said the 2005 review had made a number of recommendations - for example that scooter users should have third-party insurance, and be assessed for their fitness to drive - but that little was done.
It is calling for the government to act on findings by the Department for Transport (DfT).
The DfT said in a statement: "The 2005 review concluded that mobility scooters did not pose a significant safety risk to their users or other road users.
TYPES OF 'INVALID CARRIAGES'
Class 1 - manual wheelchairs
Class 2 - powered wheelchairs and scooters for use on pavements. Maximum speed 4mph (6.5km/h), maximum weight 113kg
Class 3 - powered wheelchairs and scooters for use on roads. Maximum speed 8mph (12.8km/h) - 4mph (6.5km/h) on pavements - maximum weight 150kg
Class 3 vehicles must be registered with the DVLA. Users do not need a driving licence or have to take a test. They do not have to pay road tax but are supposed to display a "nil duty" tax disc - which is rarely enforced. No registration plates or insurance are needed - though the latter is recommended.
"However, with the apparent increase in numbers of use of these vehicles, the department has launched a public consultation. The consultation closes on 28 May 2010."
Kevin Clinton, of the Royal Society for the Prevention of Accidents, said: "We welcome the call for data to be collected on incidents involving mobility scooters, because current evidence relating to accidents and injuries is sparse.
"The lack of such data means it is difficult to justify introducing new regulations that may be disproportionate to the level of risk associated with mobility scooters.
"It is a balance we have to get right, because mobility scooters fulfil a very valuable and important function, helping many people to enjoy a much better quality of life than they would otherwise be able to do."
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