Well, without getting too political, off road cyclists will have suffered slightly due to an act of law brought in about 2 1/2 years called NERC, a significant part of which was to "standardise" the rights of way network. Lots of routes that previously were classed as Roads Used as Public Paths (RUPPs), and Byways Open to All Traffic (BOATs) were reclassified, and in many cases were downgraded to footpath status, regardless of what evidence could prove historical usage, or to "restricted bridleways". This had the most significant impact on motorised users, as the bridleway network as it stood, except BOATs, remained largely unchanged. But some RUPPs & BOATs were lost to cycling and the local authorities won't be quick to look at usage, it is too much trouble.
The point is that the Ramblers association has a lot of political weight behind it (NERC & the "Right to Roam" being prime example). Public consultations were sought with user groups with respect to NERC, but none of the groups that represented none-walkers (CRAG, Trail Riders Fellowship, RSF etc) could get enough unity together to present a coherent front.
One group that may be trying to achieve what you describe - trying to get more access for cyclists, off road - is the International Mountain Bike Association UK (IMBA UK
http://www.imba.org.uk/ ) but you will see that they place a significant emphasis on trail building alongside rights of way access. They even have a "Rules of the Trail", which are generally good, but reflect the American roots of the organisation in the point of "Be sensitive to the soil beneath you and practice low-impact cycling. Wet and muddy trails are more vulnerable to damage, so when the trail is soft, consider riding alternative trails.". Well, thats a lot of UK mountain biking out for 11 months of the year then, isn't it?