Welshman Aaron Ramsey also extended his own deal with the club in December and Jenkinson has said that the side will benefit from the players' commitment.
"From my point of view, I think it's good to have an English core," Jenkinson told Arsenal's official website.
"The boss [Arsene Wenger] just wants the best players for Arsenal Football Club. If he thought they were [better] from elsewhere, I'm sure he would sign them.
"He obviously thinks that [by signing the British players up] we're as good or better than any other options that he had. That can only be a good thing for us.
"I think [Wenger] has said that signing young British players will [be beneficial because] they are more likely to be committed to the club and stay at the club for a long time. I think he's right in that thinking."
Arsenal are currently fifth in the Premier League.