Agapanthus 'Charlotte' is a lovely plant and (surprise!), deciduous rather than evergreen. It is just preparing for its winter's rest with leaves dying back now. It is hardier than evergreen types and will withstand winter temperatures down to -10ºC. (14ºF.). It should be just fine outdoors in London for the winter and it is important that you let it stay cool.

If it is in the ground outdoors, you can leave it there. If it is in a container, it will be more exposed than in the earth and you should give it some shelter. Put the container close to the wall of the home, in a position that is protected from winds. If temperatures drop to 0ºC. or below, insulate the container with anything at hand -- leaves, bubble wrap, newspaper, horticultural fleeces will work -- mounded or held against the pot. In ground or in a container, a layer of mulch is a good step to stabilized soil temperatures through the winter.

Courtesy of NYBG Plant Information Service