Changing terminals at Heathrow does not require you to pass the UK Border Control (there are buses) so you don't need a visa to enter the UK. The airport's website offers connection guides with the steps that will be required.
The Italian work permit could also exempt you from the Direct Airside Transit visa requirement, as explained on the gov.uk website:
You won’t need a visa if you:
- have a valid uniform format category D visa for entry to a state in the European Economic Area (EEA)
- have a valid uniform format residence permit issued by an EEA state
A uniform format visa from Italy looks like this and a uniform format residence permit like this.
If you do need to pass through the UK Border Control (e.g. to collect your luggage or stay the night in a hotel), you might also be able to get a “transit without visa concession” but that's left at the discretion of the border agent.