In the British Peerage, there are five classes (the peerages of England, Scotland, Ireland, Great Britain and Ireland and the United Kindom and Ireland) and five degrees (duke, marquess, earl, viscount and baron). Baronets (knighthoods which can be inheirited) and knights are not peers.

In 1818, there were 28 dukedoms, 32 marquessates, 210 earldoms, 66 viscounts and 172 barons – a total of 508 peerages (not including royal peerages like the earldom of Munster).[1] Included in this total are 16 ‘peeresses in their own right’. These women were the countesses of Sutherland (1235), Rothes (1457), Loudoun (1633), Orkney (1696), Antrim (1785) and de Grey (1816); the vicountesses of Massereene (1660) and Ferrard (1797); the baronesses de Ros (1264), Willoughby de Eresby (1313), Dacre (1321), Grey de Ruthyn (1324). Polworth (1697), Abercromby of Aboukir and Tullibody (1801), Sandys (1802), Barham (1805).[2]

A peer can also hold two or more separate peerages; for example, the 9^th Duke of Hamilton (in the peerage of Scotland) was also the 6^th Duke of Brandon (in the peerage of Great Britain and Ireland). Therefore, the number of peerages may be greater (for example, there were 28 ducal peerages held by 25 families).

Almost half of the 210 earldoms in 1818 had been created in the peerage of Great Britain and Ireland (97); the remaining peerages had been created in the peerage of England, Scotland and Ireland (78) and the peerage of the United Kingdom and Ireland (35). Like the ducal families, several of these families held ‘double’ earldoms.

There was a single ‘double’ viscountcy: Sir George Richard St. John, held the titles of 3^rd Viscount Bolingbroke and 4^th Viscount St. John (both created in the peerage of Great Britain and Ireland).

In addition, a peer may hold two peerages with the same name in different peerages (for example, the 1800 and 1806 baronies of Gardner or the 1776 and 1802 baronies of Rivers), This usually means the earlier title was created in the peerage of Great Britain and Ireland (pre-1801) and a similar title was later granted in the peerage of the United Kingdom and Ireland (post-1801).

These numbers do not include secondary British titles; for example, Field-Marshal Sir Arthur Wellesley, 1^st Duke of Wellington, also held the titles of 1^st Marquess of Wellington (03.10.1812) and 1^st Marquess of Douro (11.05.1814), 1^st Earl of Wellington (28.02.1812); 1^st Viscount Wellington of Talavera and of Wellington (04.09.1809) and 1st Baron Douro of Wellesley (04.09.1809).

The rules of succession in the peerage can become complicated, especially when a peer leaves no immediate heir:

“Most peerages are hereditary, meaning that they pass on from father to son, or to another heir (some peerages are created only for life, and cannot be inherited). They cannot be willed or bequeathed; how a peerage is disposed is determined by the terms of the original creation of the peerage.

A peerage passes from father to son, but sometimes a peer dies without a son to succeed him.  For example, the 6th Duke of Devonshire (1790-1858), never married.  When that happens, go back one generation, to the peer's father, in this case the 5th Duke (1748-1811), and trace the next eldest male direct lineal descendant. In this case, that would be 5th Duke's other sons, if he had any.  He didn't (at least, not a legitimate one), so we go back one more generation, to the 4th Duke (1720-1764).  The 4th Duke had at least two sons:  William, who succeeded him as 5th Duke, and Lord George Cavendish (1754-1834).  Lord George died during the 6th Duke's lifetime, but if he had survived him, he would have become the next duke.  However, he left a son, Mr. William Cavendish (1783-1812), who also died before the 6th Duke, but left one son, Mr. William Cavendish (1808-1891).  This man became the 7th Duke of Devonshire. 

But if Lord George's line had died out, then the dukedom could be traced back up to three more generations, all the way to the 1st Duke, and descend through the eldest of his other sons who had surviving legitimate male issue.  If there was no legitimate surviving male descendant, then the title of ‘Duke of Devonshire’ would become ‘extinct.’ However, if there was a legitimate surviving male descendant of his father, the 3rd Earl of Devonshire, then that person would inherit the earldom.  In this way, distant cousins can sometimes inherit lesser titles while the highest peerage dies out.”[3]

It is also important to note that extinct peerages could be ‘re-created’ by monarchs; for example, the dukedom of Leinster was created by King William III in 1691 and re-created by King George III for the 1^st Marquess of Kildare on 26.11.1766.

Notes:

[1] See Appendix 2: Errata for the British Peerage in 1818

[2] http://www.chinet.com/~laura/html/titles01.html lists 535 peers: 25 dukes, 31 marquesses, 212 earls, 69 viscounts and 193 barons.

[3] Ibid