From the text of the petition:-
"
Its not possible to book bicycle reservations online and hence one does not know whether there will be room for a bike on a train when a ticket is purchased (note, advanced tickets cannot subsequently be altered to a train with available bicycle carriage space).
"
Bike reservations can be booked online.
I do all of my travel to and from Audaxes by train and book everything through the
National Express East Coast website.
You can only book bike spaces on trains that have spaces for bikes. For the rest (like the suburban commuter trains) I just find an appropriate space and stick the bike there. I've never had a problem but then I avoid the busy times as I have no expectation to get on a train without a reservation when it's busy.
You can also only book up to about 90 days in advance. The train has to be listed as "Reservations recommended":-
http://www.greenbank.org/misc/neec1.jpg and you have to book a seat at the same time (as you need to book a specific train).
Then click on the "Bicycle space" bit when booking the seat:
http://www.greenbank.org/misc/neec2.jpg
Then you get this:-
http://www.greenbank.org/misc/neec3.jpg
The problem with the government petition system is that they wait until there's a reasonable number of signatures and then reject the petition on some technicality (like pointing out the above). After several attempts at rewriting it to fix all the problems no-one can be arsed to re-sign it.
Also, with the tin-foil hat on, in signing it (and giving valid information) you've tied your name and address to an email address; something that the Government may not have already (they've already got mine thanks to the Self-Assessment tax website and the "Government Gateway" login).
With the extra big tin-foil hat on you've also started to give them an outline of your political views. The more petitions you sign (truthfully of course) the more of a picture they get of your political views.
Of course, it's the Government, they wouldn't misuse the data at all would they.