Does anyone know if its possible to have whatever State pension you are to claim in UK transferred to CPP? Is there a mutual agreement in this regard? Also if we then decided to move back to UK, would we be able to transfer the CPP to the UK pension equivalent?

Are you talking about the Canadian Pension Plan?
I think there is some agreement but not sure how it works...i would ask someone on the Canada thread they will no doubt let you know as i'm sure there are some that are claiming pension in Canada.

Unless things have changed, a UK pension is not inflation linked in Canada. IOW, if you get 100 pounds when you move tomorrow, it'll be 100 pounds ten years from now, twenty years etc.

Bev

When you claim your UK pension as a Canadian resident you will receive it in Canadian dollars, which you will have to pay tax on as income. You will not pay any UK tax of course, as you are not a UK resident. It is not index linked. Your CPP is paid to you as normal in Canada. They are separate.

If you move to the UK, you UK pension will then be paid to you at the current rate and is index linked, and you will pay UK tax on it. You will also receive your CPP in the UK and it is index linked. You will not have to pay any Canadian tax on your CPP if you are no longer a Canadian resident, as there is a tax treaty between Canada/UK.