Sir Tim Berners-Lee, who was knighted for inventing the www network, told a conference in Edinburgh that the internet would enter a "dark period" if this was allowed to happen.
There are moves by some telecommunications companies in the United States to give priority to information from bodies which pay a fee. The idea of paying for different kinds of access to the internet has also been raised.
However, the World Wide Web Consortium, of which Sir Tim is director, and companies such as Microsoft and Google, believe in the idea of "network neutrality".
According to this guiding principle, the web, which was originally designed to allow academics to share information, should be accessible to all on an equal footing and all the information contained on it should be treated in the same way.
"What is very important from my point of view is that there is one web. Anyone that tries to chop it into two will find that their piece looks very boring. I think it is one and will remain as one," Sir Tim told the WWW2006 conference at Edinburgh International Conference Centre yesterday.
"You get this tremendous serendipity, where I can search the internet and come across a site that I did not set out to look for."
He said the correct way of running the internet was that people should pay for a connection, but not face any kind of discrimination when they searched for information.
Sir Tim invented the world wide web in 1989 while working at CERN, the European Particle Physics Laboratory, and wrote the first web client and server in 1990.