Elliot Morley, frontbench spokesman on animal welfare, issued his demand during a speech in his Scunthorpe constituency.
He said: 'When the Government introduces its law to restrict the activities of hunt saboteurs, the Labour Party will be fighting to make sure the law is completely fair so that hunts illegally entering other people's property, including road and rail, are prosecuted for trespass and hunt supporters attacking peaceful demonstrators are also prosecuted.'
Changes in the law relating to hunting form part of the Criminal Justice and Public Order Bill now before the Commons.
Mr Morley added: 'Let us also not forget that this law will divert much needed police manpower at a time of drastically increasing crime to defend a practice which causes outrage among the majority of the British people. Perhaps it would be better if the Government allowed parliamentary time for a free vote to decide whether this practice should continue.'
Nick Herbert, spokesman for the British Field Sports Society, said: 'The new law of aggravated trespass is already completely fair because it will apply to everyone, hunts and hunt saboteurs alike.
'It might have been better if Mr Morley, a frontbench spokesman, had read the Bill before making a speech about it. His call for a new law of criminal trespass to apply to railways and roads is fatuous.'