As Ethel states, any holder of an EU passport has the right to travel freely to any of the 27 member countries. (It wouldn't matter if you'd got multiple convictions for GBH, fraud and armed robbery; you'd still be entitled to travel). For a list of EU states, see here:
http://europa.eu/abc/european_countries/index_ en.htm
You'll probably have no problems with any other countries either. Some countries (outside of the EU) require UK passport holders to obtain a visa prior to travel. A few of those countries ask about
convictions on the visa application form. None ask about cautions. To the best of my knowledge, only the USA asks about arrests. (Anyone who has ever been arrested, even if totally innocent, is meant to apply for a visa before travelling to the USA. The process is lengthy, taking 5 or 6 months. Most people simply lie and say that they've never been arrested).
Enjoy your holiday ;-)
Chris