The exemptions aren't mentioned in the UK documentation because the law has already been enacted, centrally, and they have no powers over that legislation. The individual members states are in charge of monitoring, verification and punishment - that is what the UK document is concerned with.
The doc you need is this one :
EUR-Lex - 32008L0101 - EN
and the exemptions are right at the end :
This activity shall not include:
(a)flights performed exclusively for the transport, on official mission, of a reigning Monarch and his immediate family, Heads of State, Heads of Government and Government Ministers, of a country other than a Member State, where this is substantiated by an appropriate status indicator in the flight plan;
(b)military flights performed by military aircraft and customs and police flights;(c)flights related to search and rescue, firefighting flights, humanitarian flights and emergency medical service flights authorised by the appropriate competent authority;
(d)any flights performed exclusively under visual flight rules as defined in Annex 2 to the Chicago Convention;
(e)flights terminating at the aerodrome from which the aircraft has taken off and during which no intermediate landing has been made;
(f)training flights performed exclusively for the purpose of obtaining a licence, or a rating in the case of cockpit flight crew where this is substantiated by an appropriate remark in the flight plan provided that the flight does not serve for the transport of passengers and/or cargo or for the positioning or ferrying of the aircraft;
(g)flights performed exclusively for the purpose of scientific research or for the purpose of checking, testing or certifying aircraft or equipment whether airborne or ground-based;
(h)flights performed by aircraft with a certified maximum take-off mass of less than 5700 kg;
(i)flights performed in the framework of public service obligations imposed in accordance with Regulation (EEC) No 2408/92 on routes within outermost regions, as specified in Article 299(2) of the Treaty, or on routes where the capacity offered does not exceed 30000 seats per year; and
(j)flights which, but for this point, would fall within this activity, performed by a commercial air transport operator operating either:fewer than 243 flights per period for three consecutive four-month periods; orflights with total annual emissions lower than 10000 tonnes per year
In other words; anything that does not currently attract Eurocontrol will be exempt as will "small airlines".