The 34-year-old Wigglesworth replaced Ben Youngs who was forced off with a knee injury early in the 46-15 opening victory over Italy in Rome on Sunday.
Hooker Luke Cowan-Dickie was also added to the squad for the match against Wales at Twickenham on Saturday.
Number eight Nathan Hughes will join the camp this week to get his knee injury assessed.
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(Reporting by Ed Osmond; Editing by Christian Radnedge)
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