This question may seem silly, but the answer isn't obvious. According to this article from fifa.com, red and yellow cards were only introduced to the World Cup in 1970. However, the American Soccer League in the 1920's used a penalty box to temporarily remove players for illegal conduct, and players were sent off at least as early as a 1931 game between Celtic and the Hakoah All-Stars (4 players were sent off in this game.) (link) Certainly there were players ejected from games before this - does anybody know of an earlier example?
Ejections were already part of the laws of the game since the 19th century, so most likely it happened in some English or Scottish league or cup game in 18 something. They just didn't use cards.
Probably a British player yes. Some Dutch facts! The first Dutch international who was ever send off in a match was no man other than Johan Cruyff himself. It occured in just his 2nd match for Holland against Czechoslovakia on 13 September, 1966. The referee claimed that he was hit in the face by the 19 year old player although Cruyff always denied it. He wasn't shown a red card but was just asked to leave the field. At the time it was unheard of so the Dutch FA (KNVB) decided to suspend Cruyff almost a whole year for the NT. The yellow/red card system was indeed introduced by FIFA at the 1970 World Cup but the Eredivisie had to wait until the 1972/73 season. Willem van Hanegem was the first one to be booked a yellow card and the first ever player who received the red card was Issy ten Donkelaar on the 27th in August, 1972.