From its inception, it was always the aim of the EU that their should be no border controls when travelling within the member states. 25 of the members have now signed up to the relevant provisions of the Schengen Treaty, so anyone (even non-EU citizens) can travel freely between, for example, Sweden and Portugal or France and Slovakia. (That statement refers to the restrictions, or lack of them, applied by immigration authorities. Airlines and other carriers might still require some form of ID).
Only two EU countries haven't signed up to 'Schengen'. One of them, Ireland, would like to do so but it can't because it has an existing 'open border' agreement with the ONLY EU country which still refuses to sign up to Schengen. That, of course, is the UK. (Our politicians are too terrified of the rantings of the Daily Mail, etc to propose joining Schengen). So UK (and Irish citizens) have been left disadvantaged.
Even before the Schengen agreement, any EU citizen could use their national identity card, instead of a passport, to travel within the EU. (That remains true). So, for example, a French citizen doesn't need a passport to travel between France and the UK (or vice versa). He can simply show his national identity card. But, because our coalition Government has abandoned the introduction of ID cards (which would have been far cheaper than a passport) UK citizens can't do the same.
So UK citizens require a passport to travel to ANY other country (except Ireland).
Chris