As has been said your Mother’s Spouse would gain her estate as a statutory legacy in accordance with the laws of intestacy, I believe the amount is now £250K it was until quite recently (2008/2009) £125K, and he must have survived for at least 28 days, the spouse would also be entitled to her personal chattels, a definition of personal chattels can be found in S55 of the Administration of Estates act 1925.
If your Mother had died without leaving a spouse or registered civil partner but with issue you would have been eligible to your share of the estate and no distinction is made between illegitimate or legitimate children, adoptive children inherit from their adoptive parents not their birth parents.