A not-very-subtle opinion piece that tries to base itself on figures, but hey, that's not easy when you're writing the piece before looking at the figures.
"Nonetheless, the English clubs in the tournament have achieved reliability more than greatness. United have won the European Cup on three occasions, a tally that has them trailing clubs such as Ajax and Bayern Munich, never mind Real Madrid. The Anfield crowd also issues frequent reminders of Liverpool's record on that front."
Until 1997-98, only the national champion qualified for the tournament, as well as the holder of the trophy if they were from the same country. English clubs were banned for 6 seasons following the Heysel Stadium disaster, and didn't participate in 1955-56 at the FA's request. So, until 1997-98, that's 35 seasons (1956-57 to 1984-85 and 1991-92 to 1996-97). Afterwards, the numbers grew to two, three and then four teams that were accepted into the Champions' League. In contrast, Spainish and German clubs have played in 42 seasons (1955-56 to 1996-97) before non-champions were allowed to enter, and Italian and Dutch clubs 41 (Lazio was suspended in 1974-75 due to supporter violences during a clash in the previous year's UEFA Cup with Ipswich Town, Ajax was suspended in 1990-91 due to supporter violences during a clash in the previous year's UEFA Cup with Austria Wien).
English clubs have won 11 trophies (3 since 1996-97), Spanish clubs have won 12 trophies (5 since 1996-97), Italian clubs have won 12 trophies (3 since 1996-97), German clubs have won 6 trophies (2 since 1996-97) and Dutch clubs have won 6 trophies (all before 1996-97). By year in the competition, that means that upto 1996-97, the record of trophies per participation stands at : English clubs won 23% of the seasons they took part in the competition, Italian clubs 22%, Spanish clubs 17%, Dutch clubs 15% and German clubs 10%. Furthermore, one Dutch (1987-88), two Italian (1988-89 and 1989-90) and one Spanish win (1955-56) took part in seasons when English clubs did not compete, and one German win (1974-75) took part in a season when Italian clubs did not compete.
Upto 1996-97, since only the national champion and the trophy holder entered the competition the following year, a club that dominated its domestic league had more attempts to win the trophy than clubs from countries where the league was more competitive. A case example can be the Bundesliga, where Bayern Munich won 12 titles between 1963-64 (when the league was established) and 1995-96. Before the Bundesliga was started, the Oberliga champion was accepted to the European Cup, however, Bayern Munich did not win the Oberliga. In contrast, the most successful team from 1955-56 to 1995-6 (minus 1984-85 to 1989-90 due to suspension) in England was Liverpool, who won the league 10 times. However, Liverpool won the European Cup 4 times before 1996-97, whilst Bayern Munich won it only 3 times. Other clubs from these leagues support further this hypothesis. Aston villa (1 European Cup win, 1 Domestic League win), Nottingham Forest (2 ECs, 1 DL), Manchester United (1 EC, 7 DLs) on one hand, with Hamburg as the only other German club to win the EC before 1996-97 (1 EC, 4 DLs).
It seems fair to me to say that being in England meant clubs had much greater uncertainty about taking part in the European Cup in following years, as it wasn't a case of one, two or three clubs vying for the title (La Liga was won 23 times by Real and 19 times by other clubs between 1954-55 and 1995-96 ; only 11 Serie A were won in the same period by teams other than Juventus, Milan AC or Internazionale ; 17 Eredivisie for Ajax, not including the 1989-90 title, 10 for PSV and 8 for Feyenoord, 4 for all the other clubs). Liverpool and Manchester United certainly dominated (17 domestic league wins combined that qualified them for the European Cup), but 12 other clubs also won the League during this period, winning the league 18 times in total.