All sources, however, claim that
there is a hierarchy in the order of precedence, namely:
- Peers of England.
- Peers of Scotland.
- Peers of Great Britain.
- Peers of Ireland.
- Peers of the United Kingdom.
From what I understand, however, the hierarchy only applies
within the same rank , i.e. a duke always outranks e.g. an earl, no matter which peerage their titles belong to; however, among dukes, those in the Peerage of England outrank those in the Peerage of Scotland, and so on, according to the hierarchy above. Finally, within the same rank and the same peerage, precedence is determined by seniority (date of creation of the title).
An interesting point also is that the Roll of Peerage only records the
main title of British peers. There is no official directory in the UK, as far as I know, of subsidiary titles (unlike, for example, in Spain, where all existing titles and their legal holders are officially recorded). Nonetheless, the Royal Warrant of 2004 which created the Roll of the Peerage says that inclusion of the name of the title holder in the Roll is necessary to enjoy the legal rights and privileges associated with the peerage in the United Kingdom.
EDIT: After double-checking, I verified that it is actually possible to be entered in the Roll under a subsidiary title if the applicant can prove succession to that title, but not to the most senior one, but I believe that is rare. There is a more comprehensive explanation in the link below.
https://www.college-of-arms.gov.uk/peers-roll-contents