The pair were watching Alfie Hewett in action on No.1 Court, when Mr Barsdell went to get some drinks and put his plan into action.
Forty-five minutes later, after speaking with the head of security at the event and the producers for BBC Sport, Mr Barsdell returned to watch the tennis with Ms Adams, who assumed he had just bumped into someone he knew.
After the match, the couple made their way to Henman Hill, where Mr Barsdell got down on one knee.
There was tension when those watching were waiting for the answer.
“I’ve turned around with my fist in the air and said ‘she said yes’,” Mr Barsdell said.
The crowds cheered and Ms Adams said: “It was a complete surprise.”
She added: “I think it was probably easier for me because I didn’t know there were any cameras, I just heard everyone cheering and that was it. Everything else was just a blur.”
Huge tennis fan, Mr Barsdell, said he picked Wimbledon because he had been trying to get to the finals his whole life and it was a good excuse for them to “get glammed-up”.
They are hoping for a small wedding in Italy, with just close family and friends.
“Maybe we should be in tennis gear for the wedding,” Mr Barsdell joked.
“A definite no from me,” Ms Adams replied.