The pair and "Thor" actor's mother recently spent a day together in his homeland following Hiddleston's meeting with Swift's parents in Nashville.
"Tom's mom is just gushing about Taylor. She thinks Taylor is the loveliest. She was so happy to meet her," a source said.
Diana, Swift, 26, and Hiddleston were spotted walking arm-in-arm together and also visited Covehithe beach for a stroll, reported People magazine.
"Taylor was almost immediately part of the family. She was very easy to get to know and to speak with. Tom's family sees him as a big celebrity, but Taylor is clearly on another level," the source added.