Richard provided a good explanation of the process of inheriting a title in this thread:
the Roll of the House of Lords as the official record of the peerage.
When a hereditary peer dies, and his heir wishes to prove his claim to
the title, he or she must provide suitable documentary evidence to the
Crown Office of the House of Lords to prove that he or she is indeed
the heir to the title. [emphasis added]
When the House of Lords Act of 1999 removed the automatic right of
hereditary peers of England, Scotland, Great Britain and the United
Kingdom to receive a summons to take their seats in the House of
Lords, it also led to the discontinuation of the Roll of the Lords
Spiritual and Temporal. This meant that there was no official register
in which those inheriting hereditary peerages could seek inclusion as
evidence of their status and rank.
This situation was resolved by a Royal Warrant dated 1 June 2004 which
instituted a Roll of the Peerage, to be prepared and kept by the Lord
Chancellor, acting in consultation with Garter Principal King of Arms
(for English peerages) and Lord Lyon King of Arms (for Scottish
peerages). The Roll of the Peerage also records peers of Ireland and
life peers.
Any person claiming a peerage may apply to the Lord Chancellor to be
entered on the Roll; the application and supporting evidence is
presented under the direction of the Lord Chancellor. The Registrar of
the Roll of the Peerage is Ian Denyer, who is also Head of the Crown
Office at the House of Lords.
Claims to abeyant peerages, or to peerages whose succession is in
dispute, are made by Petition to The Crown, presented through the Lord
Chancellor. He refers the accompanying documents to the Attorney
General in order that he may report upon them to the Sovereign.
The Attorney General seeks the advice of Counsel for The Crown in
peerage matters and then hears the petitioner and his counsel. Claims
to peerages in abeyance will not be proceeded with if the commencement?
of the abeyance occurred more than a hundred years before the
presentation of the petition, or if the petitioner is not a child of
the last holder of the peerage or a descendant of a parent of the last
holder.
If the Attorney-General is satisfied (a) that no improper arrangement
has been entered into between the co-heirs, and (b) that no question
of law or pedigree is at issue, he may recommend the exercise of the
royal discretion without reference to the House of Lords.
Otherwise he is obliged to recommend a reference to the House of
Lords, which in turn refers the matter to the Committee for
Privileges. In the case of Scottish peerages or other peerages with a
strong Scottish connection, such claims are referred through the
Scottish authorities to Lord Lyon King of Arms.
http://www.debretts.com/people/essential-guide-to-the-peerage/claims-to-peerages.aspx