Yes, you're right, my mistake. Arundel is the oldest earldom in the UK, not Crawford. Crawford is the oldest earldom in Scotland.
Apparently Debrett's considers the Earl of Shrewsbury (1442) to be the premier earl of England because the Earl of Arundel is also Duke of Norfolk, a higher title.
It also seems that while the creation of the Crawford and Shrewsbury earldoms rests on firm ground, the history of the Arundel earldom is murkier than Wikipedia leads us to believe. For example, there is no definite record of its creation. It is believed Richard FitzAlan was created Earl in 1289. The 5th Earl died childless in 1415 and it wasn't until 1433 that his cousin John FitzAlan claimed the title belonged to whoever held the Castle of Arundel. Although the claim was dubious, the Crown allowed it.
For more details, see the Arundel entry in the Complete Peerage, especially note b on p. 231, which discusses the 1433 decision of the Crown:
https://archive.org/stream/completepeerageo01coka#page/230/mode/2up
See also the Norfolk entry in Burke's Peerage which (at the end, p. 1497) says this: "Earl of Arundel (feudal honor as adjudged in Parliament, 8 July 1433...) by possession of Arundel Castle only, without any creation."
https://archive.org/stream/burkesgenealogic1949unse#page/1496/mode/2up