I'm not sure it is 'considerable', but there are a lot of disgruntled owners of C of A Cubs.
Worse are the owners of Jodel D150s and Stampes. Here the CAA were prepared to move them to Permit, but in both cases, because one or two are used commercially (and commercial use is not possible with a Permit aircraft) they are being held on C of A.
Over the last 2 years the CAA has been looking for expressions of interest from potential TC holders. Each time the deadline for a decision was reached, the CAA extended it again.
As Rod1 says, they and EASA will not move an aircraft type to Permit if a TC holder can be found.