Setting a European record time of 3:57.50, the team of four missed out on a bronze medal by just 1.39 behind China.
Kate learnt to swim in Louth with local swimming club, the Louth Dolphins before moving to Lincoln to join a bigger club.
Australia scooped the gold and the United States came second for a silver medal.
Parents, Stuart and Caroline watched their daughter swim in Beijing from their home near Lincoln.
Stuart said: "They finished fourth and broke a record so we are all very pleased. She was a bit down about her individual but she was up yesterday, she knows she hasn't swum as fast as she could but she is just going for it now. She is going to be there in 2012 and there are a lot of big competitions coming up like the Commonwealth Games which she is looking forward to".
Kate and her team mates will now spend their remaining time in Beijing watching other Olympic events before returning home on August 26.