Well the answer to that question... is 'maybe not'. The EU and the UK Food Standards Agency have strict rules on how food is labelled. To help coeliacs, some cereals (e.g. wheat, oats) are processed to remove the gluten. If there is less than 100ppm (parts per million) of gluten remaining, the food can be labelled ‘very low gluten’. However, this level may still be too high for some coeliacs. That's where the claim ‘gluten-free’ comes in. These words can only be used where the level of gluten is 20ppm or less. This rule applies to both pre-packaged and unpackaged foods (like those bought in a restaurant, etc.).
All well and good. However, as is so often the case, it's just not that simple. Food labelled ‘gluten-free’ might still cause a reaction in a wheat allergy/intolerance sufferer because of other wheat proteins or starches present. So that's where it pays to know about your ingredients really well.
Any pre-packaged foods containing of the following allergenic ingredients must highlight it on the labelling: cereal grains containing gluten, fish, crustaceans (crabs etc.), molluscs (oysters etc.), nuts, peanuts, soybeans, milk, eggs, celery, mustard, sesame, lupin* and sulphur dioxide (at levels above 10mg/kg).
If you want to know more about labelling, see the Food Standards Agency website for more details.
*yeah, I know what you're thinking - who eats lupins? They're flowers, right? That is true, but they are also a member of the pea family, as are peanuts. Lupin flour is used across Europe in bread and cakes and this is a Europe-wide directive, which is excellent news as it makes it easier for people needing to avoid certain ingredients to travel and eat safely.