The police officers who were called to the incident decided to donate £200 to the family from the force's Tuck Shop.
Sergeant Richard Markham, from West Midlands Police, which are investigating the burglary, said:
"Stealing children's Christmas presents is such a heartless and callous thing for anyone to do. We wanted to try and put a smile back on their faces for Christmas.
"We're determined to track down whoever did this and would urge anyone with information that could help to come forward.
"If you know who is responsible please do the decent thing and call us before those responsible cause heartache like this for another family."
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Cloudy with rain or drizzle at times, locally heavy over higher ground in Shropshire and Staffordshire.