No, you have to actually own the property in order to use it for the accommodation requirement... which means you need to provide the Land Registry document that lists you as the owner... and you won't have that until a month or two after you have purchased the property.
I bought a house last year - we exchanged contracts mid-March, I got the keys end-March, moved in early April and got my Land Registry document around late April, I think, maybe early May.
A mortgage in principal doesn't really mean anything in regards to owning - it just confirms that the mortgage lender has agreed to give you the money when you actually buy the house.
Really, the only thing you can do is use your parents' house for the accommodation requirement and see if you can sort out exactly who owns it and who needs to provide the letter giving permission for you to live there too.
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