Sportal.co.nz 20.Nov.2012Getty Images
The Springboks accounted for Scotland 21-10 at Murrayfield on Saturday, while England went down to Australia 20-14.
"England will be even more motivated [after the defeat]," Meyer told BBC Sport.
"Saturday will be the ultimate test. England has a great team and we've got a lot of respect for them.
"They are always much better at Twickenham.
"They have moved on [under coach Stuart Lancaster] and are trying to play a more expansive game.
"He is a great coach and he'll definitely go places."
Lancaster appears set to make several changes to the side to face South Africa after England failed to fire up front against the Wallabies.
Joe Marler remains in doubt with a knee injury, though fellow prop Alex Corbesiero could return from a knee complaint of his own.
"The priority now is to get the selection right, with the physicality of the Springboks," Lancaster told Sky Sports. "Changes in personnel will give us some impetus.
"Ben Morgan scored a hat-trick [for Gloucester] at the weekend, James Haskell is desperate for an opportunity, Tom Wood is ready for a start, Alex Corbesiero is coming back.
"They will come into the equation."