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It depends a bit on the line, but the mainline trains from Norwich - London have space for six bikes (I've seen 8 before) in the carriage (which is the same as they always claimed for the old trains, although obviously you could physically fit more). It's one of the better bike setups I've seen in the new trains that have come out in the last few years as you don't have to hang them up.
They have changed the rolling stock recently. The old ones had two massive guards vans, one at each end of the train. The new rolling stock has space for 2 bikes or something day, so they simply have no way to fit large numbers of bikes onto the new trains. They did quite a long blog post on their website about a year ago. In the past they've been really supportive of the event, but without those older style trains, it's no longer possible.