A woman in her 20s and a two-year-old girl were found at an address in Woodthorpe Road with serious injuries yesterday lunchtime.
The woman died at the scene while the toddler was taken to hospital.
A man in his 30s, known to the victims, is being questioned by police.
Statement from Cllr Joanne Sexton, Leader of Spelthorne Borough Council:
“I am truly shocked at this devastating news. I recognise this is a very worrying time for residents but please be assured that there is no wider risk to the community, however I do urge anyone who can assist with the investigation to get in touch with the police. As a matter of course, the Council will be holding a meeting to review this incident and offer our ongoing support to the wider community.
My thoughts are with everyone affected during this sad time.”
