Hi foreverawhite,
If the policy is for 'brand new customers only' then no, you will not be entitled to it as it is the same insured item!!
All these cashback deals are a waste of time anyway. It's a gimmick - and it works, sadly!! I can't see Barclays being the cheapest insurer for home and contents - not by a long shot!! Try calling a broker who has lots to look at - remember Barclays just look at one product.