Rachel immediately said yes and gushed: "I really didn't have a clue he was going to do it and am thrilled to pieces. We are both so happy."
The singer announced her engagement to a newspaper on Sunday before S Club 7 performed at London's Wembley Arena.
Jeremy, 31, plays Danny Shaugnessy in Holby City.
The couple have been dating for 18 months but Rachel says she had her eye on Jeremy since his days in the Channel 4 soap Hollyoaks.
They haven't set a date for the wedding yet.