not require any kind of passport or identity when traveling between countries before the year 1914?
YES Well maybe not require but passports helped with proving one's nationality for at least 500 years before the quoted British Nationality and Status of Aliens Act 1914.
According to this Wikipedia article:
King Henry V of England [who reigned from
21 March 1413 to 31 August 1422]
is credited with having invented what some consider the first passport in the modern sense, as a means of helping his subjects prove who they were in foreign lands. The earliest reference to these documents is found in the Safe Conducts Act 1414 (caution: one of the options within this link is to the Act's original text which includes a pdf that is over 50mb with 855 pages which I have yet to read).
In 1540, granting travel documents in England became a role of the Privy Council of England, and it was around this time that the term "passport" was introduced.
In Scotland, passports were issued by the Scottish Crown and could also issued on the Crown's behalf by burghs, senior churchmen and noblemen.
Passports were still signed by the monarch until 1685, when the Secretary of State could sign them instead. The Secretary of State signed all passports in place of the monarch from 1794 onwards, at which time formal records started to be kept; all of these records still exist.
Passports were written in Latin or English until 1772, then in French until 1858. Since that time, they have been written in English, with some sections translated into French.
In 1855, passports became a standardised document issued solely to British nationals. They were a simple single-sheet hand-drafted paper document.
The Wikipedia article also includes images of British passports from 1857 and 1862, but having a photograph of the holder wasn't introduced until 1914/15.