More than 2,700 signed the e-petition, on the 10 Downing Street website.
It said: "Canoeists and un-powered craft users are seeking the right to roam on English and Welsh rivers. This is without consultation with landowners.
"This, in our view, will be detrimental to river systems and will spoil the enjoyment of the rivers for anglers. Angling clubs already pay rent to landowners for using the rivers as well as anglers paying national rod license fees. The canoeists want the right to spoil our enjoyment for free."
Today those who signed up online, who included members of the Pike Anglers Club of Great Britain, were told the campaign had succeeded.
In a statement posted on the 10 Downing Street website, Tony Blair's office said: "Research we have undertaken has shown that there is not a demand for access to all inland water, and it is therefore impossible to justify legislation to deliver this, which would undoubtedly be complex, controversial and costly.
"Our conclusion from the evidence is that demand for access would more effectively be met by a targeted approach, which involves identifying where access is needed, and then creating access agreements with the landowner and other interested parties.
"Another benefit of this approach is that it results in access arrangements that are clear and can be codified so that everyone knows what can, and cannot, be done under the agreement. We believe that this sort of arrangement would be welcomed by landowners and by most water users.
"To help identify the demand for water access we have asked the Environment Agency to work with other stakeholders to draw up strategic plans. Draft plans for two of their regions - the South-West and East of England - should be published for consultation by the end of the year. The Agency is also prepared to work with user groups to help identify specific sites where an access agreement might be put in place.
"Creating access via agreements will undoubtedly require goodwill and hard work on all sides and nothing will be achieved overnight. But we firmly believe that this is the right approach. Given the commitment of all interested parties, particularly water users and landowners, this managed and targeted approach should, over time, result in a significant increase in the amount of inland water accessible to all water users."Click here for more on this story.