1952 Adoption Act - Property Rights
(2) In any disposition of real or personal property made, whether by instrument inter vivos or by will (including codicil), after the date of an adoption order—
( b ) any reference (whether express or implied) to the child or children of the adopted person's natural parents or either of them shall, unless the contrary intention appears, be construed as not being, or as not including, a reference to the adopted person;
Scroll up to post #9 above, which is the section from the 1952 Adoption Act referring to property rights in the case of intestacy.
It is clear that, once the subject of an Adoption Order under the 1952 Act, there is no legal entitlement to anything from a natural parent's estate.
However, as 3littlefish pointed out, should you inherit from a natural parent's estate, your liability to CAT is calculated on the basis of a Group A relationship in terms of thresholds etc.