Constitutional significance of HRAWatch
I know cases for S3 and S4 of the HRA and the significance, but not sure what cases to use for Parliamentary sovereignty for constitutional significance in HRA
I have few cases which I dont know how to apply for this question:
R (on the application of HS2) v. Sec. of State for Transport  UKSC 3
Kennedy v Charity Commision
Thornburn v Sunderland
and which cases should I use to demonstrate parliamentary sovereignty
Sarcastic response aside, your question is not particularly clear. You have repeated the question about cases demonstrating sovereignty; it is not clear if these requests are in some way separate. There are a host of cases in which HRA is applied (as you might suspect), in so many arenas (private contracts, employment contracts; not just public law stuff).
Do you want all these cases provided to you by us? Cases which demonstrate sovereignty? Well, there are cases which interact with the idea but sovereignty is an autonomous concept. Quote Dicey (as everyone else with, read an article criticising that description) and then proceed with those cases which interact with the concept. Point to cases where HRA is used, how incompatibility is more common in the big cases than interpretation. Doesn't this go against the notion that the judiciary will not legislate; will not infringe upon Parl's power to legislate? Well, no, because Parl gave courts this power and can take it away at any point.
Go from first principles.
An excellent and informative post.