Mnay more people seem to be interested in pulling trailers behind their bikes, but the cost of a bike specific trailer (i.e. under 1 metre wide) is very high.
However, if you are prepared to make the chassis yourself, then you could do a lot worse then going to Halfords for the box. They do a narrow short roof box (240L) for £99 (reduced from £140). It is rear-opening and looks ideal for the purpose.
Cheers
GC