However Bradley acted fast and secured the signatures of Cardiff Blues scrum-half Richie Rees and prop John Yapp to plug the gap.
This brings the number of players lined up to join Edinburgh next season to five, with prop WP Nel and Northampton Saints' Greig Tonks having already agreed to a move, as the club look to take their Heineken Cup form, where they have reached the final four, into the RaboDirect PRO12, where they currently sit second from bottom.
And Bradley is convinced his new recruits will help the Gunners do just that, having seen competition for places work wonders for the two clubs challenging for the Premier League title.
"Strong internal competition is the format for every successful side," Bradley told the Daily Record.
"If you go into football, United and City are the top two in the Premier League and have international players coming and going, left right and centre.
"Richie is a very good all-round player who has an eye for a break. That ability is an important element to any scrum-half who comes to Edinburgh. He is a confidence player and we look forward to working with him next season.
"Like Richie, John is an experienced international. The front row is an area we're looking to strengthen.
"He's 6ft 2in, 19 stone and was involved last year with Wales. What impressed me about him was that he was looking for a new challenge because he's been with Cardiff for a long time."