Sian Duili, 47, and daughter Aisha were last seen in Barry on Tuesday and were believed to have travelled north.
That was confirmed when CCTV footage emerged of them shopping in a Gretna branch of Costcutter.
They were in the shop at around 1.15pm on Thursday, 30 minutes after they were also sighted in Carlisle, according to Wales Online.
South Wales Police said concerns are growing for their welfare and officers are appealing to the public to help track them down.
Sian is believed to be travelling in a white Kia Sportage car, registration number CE67 RPZ
Superintendent Alun Morgan said: “We are becoming increasingly concerned for Sian and Aisha.
“We are now very worried for their safety as no contact has been made.
“I am grateful for the support of officers around the country in assisting with extensive enquiries and we are working more closely with Police Scotland and north of England forces to help locate Sian and Aisha.
“I’d like to make a direct appeal to Sian to get in touch with us so that we can make sure that Sian and Aisha are both safe.
“Friends and family are also extremely concerned.
“I’d also like to ask the public to help us find them.”Anyone with any information on their whereabouts should contact 101, quoting reference 1800467620.