English teams in early international club competitions

Clapton FC were the first British club to play on the continent. In 1890 they traveled to Antwerp and beat a Belgian XI 8-1.

Following this groundbreaking  trip it became increasingly common for British clubs to play abroad. Usually these fixtures were part of friendly summer tours that had a missionary purpose. Continental teams were keen for the prestige of playing against British clubs and viewed the experience of getting thrashed by some amateurs on a jolly as a valuable learning experience.
When the mania for football on the continent reached the point where the idea of international club competitions was being explored, major British teams were absent, and the results of friendly fixtures at the time reveals the gulf that existed between British and continental football (just a few examples: 1894: Standard Athletic Paris 1, Belsice 8; 1900: Racing Club Paris 1, Barnes 3; 1901: Germany XI 2, Aston Villa 6; S Brugeois 0, Cambridge University 4; 1904: Select Paris 2, Newcastle United 11; Union Saint Gilloise 1, Tottenham Hotspur 8; Karlsruher FV 0, Newcastle United 7). 
1909 was the watershed year, with two English amateur sides competing in tournaments on the continent.

The Challenge International du Nord had first been contested by French and Belgian clubs in 1898 with Dutch and Swiss teams joining in 1905.

When, in 1909, England sent a representative to this tournament it wasn't league champions Newcastle United or FA Cup winners Manchester United who went, but rather Eastbourne FC of the Southern Amateur Football League.
Entering at the semi final stage they beat Le Havre Sports (2-0) and Racing Club Roubaix (5-1) to win the trophy.

Reigate Priory

 Reigate Priory (also of Southern Amateur Football League, and relegated from the Senior A section that season) repeated the success in 1910, with Cambridge Town (another Southern Amateur Football League outfit in only their third season) losing the 1911 final, winning the trophy in 1912 reaching the semi finals in 1913.

In 1909 Sir Thomas Lipton (who had donated a trophy to be played for between Argentina and Uruguay from 1905) sponsored an international club tournament, held in Turin. The FA didn't want anything to do with it, so Sir Thomas invited West Auckland of the Northern league to represent England.

West Auckland

Other teams in the 1909 tournament were Torino XI (Italy, a combined Torino / Juventus team), Stuttgarter Sportfreunde (Germany) and FC Winterthur (Switzerland). West Auckland beat Stuttgarter and Winterthur, both by 2-0, to lift the trophy.
in 1911 West Aukland were invited to defend the trophy. In Turin were joined by Juventus and Torino (Italy) and FC Zurich (Switzerland). West Aukland successfully defended the title, retaining the trophy in perpetuity. Having seen off FC Zurich in the first round they beat Juventus 6-1 in the final.