How is the English royal family related to the Swedish royal family?

Yes, Because the wife of King Edward VII before Prince of Wales was Princess Alexandra of Denmark who was the daughter of then King Christian IX and their decendants are close cousins

The Danish Royal Family is also related to Royal Families of Spain and Greece because Queen Margarethe II's sister then Princess Anne-Marie of Denamrk married then Crown Prince Constantine and eventually became the King and Queen of Greece.

King Constantine's sister then Princess Sophie of Greece of Denmark married then Prince Juan Carlos of Spain to eventually become The King and Queen of Spain.

Today they are all closley related