The Ministry of Justice says that handsets smuggled into jails are being used by offenders to harass victims, organise gangs and deal drugs on the outside.
It has already carried out trials of jamming equipment, which is illegal if used in public, and is about to give portable devices to some prison governors.
And next week the Government will back a Bill proposed by a Conservative MP that would allow the authorities to track mobile calls attempted by criminals as well as stop them getting through to their associates.
It follows a series of reports by officials and experts warning that phones are being used to plan crimes and smuggle drugs into prisons.
"Mobile telephones are used for a range of criminal purposes in these institutions, including commissioning serious violence, harassing victims and continuing involvement in extremist networks, organised crime and gang activity. Access to mobile telephones is also strongly associated with drug supply, violence and bullying."
It is already against the law to take mobile phones into prisons or young offender institutions or to use them within their walls, but they still find their way in thanks to inmates, their visitors and corrupt staff.
Recent figures show that 40 mobiles were found at one prison, HMP Wakefield, in just nine months, when staff and visitors were searched at the gates. Many of the SIM cards were taken out and sent to a central unit to be analysed.
"These trials have demonstrated that equipment can be capable of denying signals to illicit mobile phones within the prison perimeter as required by law and Ofcom regulations, but that this is not a quick, simple or cheap solution," said Crispin Blunt, the prisons minister. One expert claimed it would cost £250,000 to block signals at a single jail.
The minister added that "a number of short range portable mobile phone blocking devices" have also been purchased.
His Prisons (Interference with Wireless Telegraphy) Bill, to be debated in the Commons next Friday, will allow ministers to let prison governors "interfere with wireless telegraphy" in order to prevent the use of mobile phones, and also to "investigate the use of such devices".
"The provisions of the Bill are designed to create a clear and transparent legal basis on which signal interference equipment can be used within relevant institutions to enable the authorities to find mobile telephones and to disrupt, by means of signal interference equipment, the use of those telephones that cannot be found," according to the MoJ's note on the Bill.
Sir Paul told a local newspaper he was inspired to draft the Bill after seeing a mobile phone jammer used in a noisy train carriage.
"I was sitting on the train on the way home and several people were making pointless and annoying calls in loud voices," he said.
"Things like 'hi mum, I'm on the train, I was on the same train yesterday, what's for dinner?'
"These calls were driving a number of us up the wall and a guy got this little thing out and flicked a switch and stopped all the conversations. It is illegal but it was very funny."
Ofcom, the communications industry regulator, said it believed prisons could use mobile jammers within their walls because they are Crown property.
A Ministry of Justice spokesman said: "Illicit mobile phone possession in prison is a very serious offence and is dealt with appropriately.
"This bill will grant new powers to prison authorities so that they can block mobile phone signals within the prison walls.
"Technology to locate smuggled mobile devices or render them useless is improving and will play an increasing role in tackling this illegal activity in the future."