Also among the athletes to return home was gymnast Bryony Page, who won trampoline gold to secure a complete set of medals after silver in Rio in 2016 and bronze in Tokyo in 2021.
The 33-year-old was a Team GB flagbearer for the closing ceremony alongside triathlete Alex Yee.
“It hasn’t sunk in,” Page told BBC Sport. “My coach said it quite nicely: I have a whole lifetime for it to sink in. I am going to be an Olympic champion for the rest of my life.
“This whole Games has been an amazing experience. To be part of this team for the third time is just phenomenal.”
Rutter, who became a mother in April, said she was thrilled to be coming home to her family with an Olympic medal.
“It feels incredible,” she said. “It’s something at one point I never thought I would achieve, so I’m super happy.
“I’m so happy to be back. Just to see this little guy is the best thing.”
An emotional Tom Daley, who has announced his retirement from diving after winning his fifth Olympic medal in Paris, said: “Right now, I’m really happy with how everything’s gone. I just think it’s always hard when you say goodbye to your sport. Lots of things to process, but I think it’s the right time.
“This year felt like such a bonus and I got to compete in front of my family, my kids. I got to be flagbearer. So yeah, bucket list ticked off on every occasion.”