I've been reading some research papers about p53 and associated tumour suppressor proteins, such as p21. I see them referred to and associated with cyclin-dependent kinases. Is p53,p63 et cetera part of the CDK family?
No, p53 and other tumor suppressor proteins do not belong to Cyclin dependent kinase(CDK)family. p53 blocks the cell cycle by promoting the synthesis of Cyclin dependent kinase inhibitors (CKI proteins). These CKI proteins bind with the Cyclin and CDK complex and inhibit the cell cycle at G1 checkpoint.
p53 also plays role in activating DNA repair enzymes and if DNA is not repaired, p53 will promote apoptosis, so that defective DNA is not passed on.
These all proteins are structurally homologous to p53, so together they are known as p53 family.