First of all, I would challenge whether they can reduce your Prices. They are imposing a further constraint that is forcing you to use this Subsubcontractor, but you could choose to use this Subcontractor off your own bat and the Prices would stay the same.
However, you are presumably choosing to use the other more expensive one because they are reliable etc which de-risks the rest of your contract. Consequently, this additional constraint, you could argue is introducing risk for which you could charge under clause 63.6.
See how the Contractor responds to that !