Police swooped on the home on Hotchkin Avenue in the village this morning.
It is thought that Muslim convert Michael Adebolajo - one of the suspects in the attack - was registered as living at the address in 2003.
“We knew nothing about it until about 9.30am this morning when I saw a police car blocking the road,” said local resident George Martin.
“You just don’t think things like this will happen in a place like this.”
“It was a barbaric attack and is shocking to think someone involved in it may have lived her in Saxilby.”
Another resident, who did not wish to be named, said they couldn’t believe it when they heard the news.
“This is a quiet, peaceful place. Not a place connected with terrorism.”