Clarke, the Bath back-row forward, strained his back and the prop Leonard aggravated an ankle injury he picked up playing for Harlequins a fortnight ago.
Their participation in England's opening Five Nations match in Dublin in three weeks' time is not yet in doubt, but they will be making only limited contributions to the remaining five sessions in the Canaries.
Clarke said: "I have had back trouble before and it should be OK soon." Meanwhile, Leonard, who has played 34 consecutive Tests since being capped in Argentina, was immediately carried off to the treatment room but had to wait for the physiotherapist Kevin Murphy to finish with Clarke. Murphy said: "Jason's ankle is swollen but I hope to have him walking around tomorrow."
The injuries will hinder England full training sessions this weekend. There are now only three fit props and Jack Rowell, the manager, said: "We will have to use the scrumaging machine or switch the third hooker, Mark Regan, to prop if we want live scrumpractice. Ben's problem, though, is taken care of by the fact that we have seven back-row forwards here."
If Leonard's ankle proves a prolonged worry, Graham Rowntree would win his first cap. If Clarke remains unfit, on the other hand, it would solve Rowell's back-row dilemma, which he describes as "an embarrassment of Richards". Either Steve Ojomoh or Neil Back would step in at open-side flanker.
Paul Hull was an injury worry England brought with them. He has not played since coming off against Canada three weeks ago and, after warming up yesterday, did a few laps of the track here. "Paul is proving that Achilles tendon injuries hang around," Rowell said.
Hull needs to improve rapidly if he is not to be left out when England name the team to play Ireland. That announcement is planned for the week beginning 9 January.
Mike Catt, without wishing Hull to lose a cap, has expressed an interest in the full-back position he filled in scoring two tries when coming on for Hull against Canada. "I want to play for England anywhere," the Bath stand-off said. Rowell commented: "Mike is front-runner if we need to change our full-back, but we also have Jonathan Callard here."