Pulsatilla vulgaris @Chris Cheffings/JNCCThe Wildlife and Countryside Act 1981 includes a number of plants in Schedule 8.  All of these designations are also available in the Species Designations Database.  It is an offence to pick, uproot, trade in, or possess for the purpose of trade, any of the designated species.  The exception to this is the bluebell, for which it is only an offence to trade in the species or to possess it for the purpose of trade.
Plants are included in Annexes II, IV and V of the EC Habitats Directive.  These designations are available in the Species Designations Database.  Annex II includes those plant species of community interest for which special areas of conservation shall be set up under the title Natura 2000.  This network, shall enable the species' habitats to be maintained or, where appropriate, restored at a favourable conservation status in their natural range.  Annex IV includes those plant species which have strict protection, prohibiting the deliberate picking, collecting, cutting, uprooting or destruction of such plants in their natural range in the wild; and the keeping, transport and sale or exchange and offering for sale or exchange of specimens of such species taken in the wild.  Annex V includes those plant species of community interest whose taking in the wild and exploitation may be subject to management measures.  The UK is required to conduct surveillance of the conservation status of all of these species, and is further required to report on the conservation status every six years.
Information about the inclusion of plants on CITES can be obtained from the Royal Botanic Gardens Kew.  Kew acts as the UK CITES Scientific Authority for Plants.