It followed a row between Reform UK and the government about the level of security provided to its leader Nigel Farage.
Reform UK’s Treasury spokesman Robert Jenrick had made accusations of a “dereliction of duty”.
He claimed Farage had not been given the security he needed, after it emerged Reform turned down a government-funded security offer last year.
The Home Office said Jenrick’s comments were “categorically untrue” and that ministers were not responsible for deciding MPs’ security.
Politicians’ safety had already become a big concern after the murders of Conservative MP Sir David Amess in 2021 and Labour MP Jo Cox in 2016.
In May 2024 the Conservative government announced a £31m package to increase security.
The two police initiatives mentioned by Polanski are national drives to “strengthen the safety and security” of people in prominent roles.
Former head of counter-terrorism policing Neil Basu warned on Tuesday a high level of protection to all 650 MPs would need “thousands” of new police officers to be recruited.
Widdecombe was found dead in her home last Thursday after police believe she was attacked there a day earlier.
A white British man, 28, arrested on Saturday in South Yorkshire, is being held on suspicion of murder and on suspicion of commission, preparation or instigation of acts of terrorism.