When on a jar of jam is written without additives and artificial colours, are there really no additives inside or does the law allow certain concentrations without labelling?

Germany

The use of food additives must always be labelled on the packaging of food products by their category (anti-oxidant, preservative, colour, etc) with either their name or corresponding E-number. Community legislation on the labelling of foodstuffs includes general provisions on the labelling of foodstuffs to be delivered to the consumer, as laid out in European Parliament and Council Directive 2000/13/EC. All food additives must have not only a demonstrated useful purpose but also a thorough and rigorous scientific safety evaluation before they can be approved for use. The E-number signifies approval of an additive by the EU.

Read:

Community legislation on the labelling of foodstuffs
http://europa.eu.int/comm/food/food/labellingnutrition/foodlabelling/comm_legisl_en.htm