Will register include 'charities' as well as businesses?
There a number of groups which are registered as charities who lobby heavily. Environmental charities such as FOE are one example, but political groups who are registered as charities because they're non profit making.
If the register doesn't include 'charitable' lobbying it isn't very useful. All that will happen is that the lobbying will be routed through a 'front' charity to avoid the register.