The incident happened on October 21.
Gary Cooper, 55, of Odstock Road has been charged with two counts of dwelling burglary and theft and fraud by false representation.
He has been remanded in custody and is due to appear at Swindon Magistrates Court this morning.
The second charge of burglary and fraud relates to an incident on October 14 in Trowbridge in which a debit card was stolen from an address and used to obtain cash and goods.
A second man has also been charged in relation to this offence.
Jamie Kerley, 31, also of Odstock Road, has been charged with fraud by false representation and handling stolen goods.
He has also been remanded in custody and is due to appear at Swindon Magistrates Court this morning.
Det Sgt Anthony King, of the Operation Fortitude team, said: “These charges are an example of the great work being carried out by the Operation Fortitude unit, which has been set up to target offenders who prey on vulnerable people within our communities to commit crime. Distraction burglary can have a devastating effect on vulnerable people and the consequences can be devastating for them and their families. “
If you suspect any suspicious activity or cold calling in your neighbourhood, please call police on 999 if a crime is in progress or 101 to report concerns.