Yes, Buildersmate has a valid point. I probably scanned your question too quickly, noting only the reference for "no need for probate" rather than the words "in common".
If you bought the property as 'joint tenants' neither of you owned a specific share of the house. It was your legal partnership which owned the property. As the sole surviving partner you now own all of the house, with no to seek a grant of representation in respect of your mother's estate.
However if you were 'tenants in common' you each owned a specific share of the house (which would have been a half unless otherwise specified). Your mother was entitled to leave her share to ever she chose, so you'll need to show that you've rightfully inherited that share of the property. That means applying for a grant of probate (if she left a will) or for letters of administration (if she died intestate).
Chris