If you had been joint tenants then, upon the death of one of you, the whole of the cottage would automatically have been transferred to the surviving partner. No part of the cottage would form part of the deceased partner's estate. So probate might not have been required.
But, as tenants in common, (normally) half of the value of the cottage will form part of the deceased partner's estate, taking it well above the £5000 threshold where a grant of probate is required:
http://www.direct.gov...eparation/DG_10029799
Chris