the first team to play in a European competition that was british was Hibernian
Manchester United in the European Club Champions Cup.
Celtic F.C. were the first British club to win the European cup in 1967
Celtic was the first team to win.
Tottenham, winners of the 1963 Cup Winners' Cup.
The UEFA European football championship was inaugurated in 1955 in Paris, at the suggestion of the French sports journalist and editor of L'Équipe Gabriel Hanot as a continental competition for winners of the European national football leagues, as the European Champion Clubs' Cup, abbreviated to European Cup. http://www.myfootballfacts.com/EuropeanCompetition.html
Leeds, winning the 1968 and 1971 Fairs Cups.
Liverpool F.C won the UEFA Cup in 1973 then the European Cup in 1977
The UEFA European Football Championship was first held in 1960.