Under the EC Regulation 261/2004 if your flight was cancelled or you were denied boarding, you have a right to financial compensation.
In case of a flight delay, you can claim financial compensation on the basis of the Court of Justice of the European Union decision from 19 November 2009. This decision shook the air carriers' world, which used to classify a majority of flight disruptions as 'delays' in order to avoid payment of compensation to passengers. Some of the English airlines went as far as to apply for a judicial review to the High Court of Justice. As a consequence the High Court of Justice posed some questions to the Court of Justice of the European Union. The answers were given by the Court of Justice in 2012 in which it confirmed that in cases of a significant (over 3 hours) flight delays, the passengers are entitled to financial compensation specified in the EC Regulation 261/2004.
If you claim under the EC Regulation 261/2004 the national law of limitation applies. In England and Wales you can claim for flight disruptions which occurred not longer than 6 years ago.
Here are the links to the Acts you may wish to rely on when making a claim against the air carrier:
Regulation (EC) No 261/2004 dated 11 February 2004
Carriage by Air Acts (Implementation of the Montreal Convention 1999) Order 2002/263