What are cycle spaces, and where do Tandem and Trailer go?
I think it would be good if a standard bicycle were defined. If the standard bicycle doesn't fit easily in all the cycle spaces, they are not cycle spaces. The standard bicycle should be large - I suggest the largest-framed men's roadster commonly available, with the seat and handlebars as high as they go.
I'm ambivalent about whether the bikes hang vertically from hooks or are supported horizontally. The key points to me are consistency and that a large adult bicycle fits easily.
If trailers can be detached and in some way folded or dismantled such that they are the size of a large suitcase, no special provision is needed. Otherwise, a bike+trailer could be considered as a tandem.
I think that solo cycles should be carried on every train (although on peak-time commuting trains there would only be a small number of spaces, which must be paid for). Although it would be nice, it is not so important to me that tandems be carried on every train. Instead, I think that it should be possible to get from any GB station to any other one with a tandem, although this might require taking a slower route or travelling at certain times of day.