Can anyone suggest a way to mount my rack to prevent it impeding the rear brake? I have a topeak rear rack the mounting of which is interfering with the operation of the rear brake. 

Unfortunately, my frame (a 2009 Scott Sportster P4) only has mounting lugs on the outside of the seatstay meaning that the rack's mounting arms just touch the outside of metal sheath around the brake cable. The brakes still apply but the cable is not free to move as it should be. A pretty standard V-brake setup. 

Does anyone have any good ideas for a mounting solution that would enable me to mount the rack in such a way that the mounting arms bend in more quickly to avoid the brakes?

I'm tempted to heat up the arms and bend them with a wrench - any concerns or recommendations?
You shouldn't even need to heat up the arms.  Just bend them whichever way you'd like; it's easiest if you have access to a vice.  You might even look at having them make an 'X', if that pulls the mounting arm away from the brake.   By design, the horizontal stays should have a minimum amount of force on them - they handle keeping the rack from rotating forward and aft while the bulk of the weight is transmitted down the vertical stays.

You could also get p-clamps and attach the rack stays lower or higher as needed to clear the brake.