The visitors took the lead through Tim Payne and Haskell before Brock James kicked Clermont eight points clear.
Northampton's Ben Foden and Wasps prop Tim Payne have also joined the England squad for training this week.
Standing opposite is an English front row with 80 caps shared between Tim Payne, Steve Thompson and Dan Cole.
The only enforced change sees Tim Payne replace Andrew Sheridan at loose-head.
However Wasps struggled in the scrum, with New Zealand referee Bryce Lawrence having a word with England loosehead prop Tim Payne after two scrums collapsed.
The match turned nasty on the hour mark when Canadian flanker Jamie Cudmore unleashed a flurry of punches on Wasps prop Tim Payne, sparking a brawl.
But the match went to uncontested scrums after loose-head Black was forced off only for replacement Murphy to join him with a shoulder injury after just one set-piece against powerful Tim Payne.
The others are Leicester duo Anthony Allen and George Chuter, Wasps pair Joe Worsley and Tim Payne, Gloucester's James Simpson-Daniel and Paul Doran-Jones, Saracens wing David Strettle and Harlequins flanker Chris Robshaw.
He spoke to Tim Payne, a US soldier who lost both legs in Afghanistan last year, who told the prince that coping with his injuries was a case of "all mind over matter".
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And, given all the errors, it was hardly surprising that frustration would kick-in at some point, a fact illustrated when Wasps' England prop Tim Payne and Gloucester number eight Brett Deacon traded blows.
Cole has flourished this term in the absence of injured veteran Julian White, and cemented his reputation as a Test prop-in-waiting by demolishing Wasps loose-head Tim Payne in the scrum in a Premiership match last month.
Among the forwards, there could be a first cap for Wasps' Tim Payne at loosehead prop, but Woodward at least has plenty of back-row cover, with Martin Corry, Michael Lipman and Chris Jones all vying for starting places.
England's front-row resources were severely stretched during the autumn Tests, with Bath's David Wilson and Duncan Bell and Wasps' Tim Payne filling in for the absent Vickery and Andrew Sheridan, while the inexperienced Paul Doran-Jones was called on to cover the bench.
The other players released to play for their clubs in the EDF Energy Cup this weekend were Gloucester centre Olly Barkley, Leicester trio George Chuter, Jordan Crane and Dan Hipkiss, London Irish duo Shane Geraghty and Peter Richards, and Wasps prop Tim Payne.
Wasps followed up their victory over Harlequins at Twickenham on the opening weekend of the season by hanging on with 14 men after their England prop Tim Payne was sent off having received two yellow cards for separate scrum offences in the closing stages.
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