Current laws which only proscribe the use of devices being held by drivers gives the "misleading impression" that hands-free use is safe despite it creating "the same risks of a collision", a report published by the Commons Transport Select Committee warned.
The cross-party committee acknowledged that there would be practical challenges to criminalising hands-free phone use and enforcing the offence, but insisted "this does not mean that we should not do it".
It recommended that the Government should explore options for extending the current ban on hand-held mobiles and publish a public consultation on the issue by the end of 2019.
In 2017, there were 773 casualties on Britain's roads - including 43 deaths and 135 serious injuries - in crashes where a driver using a mobile was a contributory factor.
The committee said the number of people killed or seriously injured in such accidents has risen steadily since 2011 but the rate of enforcement of the law regarding phone use has plunged by more than two-thirds since the same year.
Since March 2017, motorists caught using a hand-held phone have faced incurring six points on their licence and a £200 fine - up from the previous penalty of three points and £100.
The MPs urged the Government to consider whether penalties should be increased further "to better reflect the serious risks created by drivers committing this offence".
Labour MP Lilian Greenwood, who chairs the committee, said: "Despite the real risk of catastrophic consequences for themselves, their passengers and other road users, far too many drivers continue to break the law by using hand-held mobile phones.
"If mobile phone use while driving is to become as socially unacceptable as drink-driving, much more effort needs to go into educating drivers about the risks and consequences of using a phone behind the wheel.
"Offenders also need to know there is a credible risk of being caught, and that there are serious consequences for being caught.
"There is also a misleading impression that hands-free use is safe. The reality is that any use of a phone distracts from a driver's ability to pay full attention and the Government should consider extending the ban to reflect this."
RAC head of roads policy Nicholas Lyes said: "We support the committee's call for the Government to look more closely at the effectiveness of the increase of the penalties in 2017, and key to this is whether enforcement is adequate and whether the police have sufficient resources and technology to be able to crack down on this scourge."
A Department for Transport spokeswoman said: "While mobile phones are a vital part of modern life and business, drivers must always use them safely and responsibly.
"Being distracted by a mobile phone while driving is dangerous and puts people's lives at risk. The law is clear that anyone driving dangerously is committing a criminal offence."