For example, Virgin Media have been facing accusations of blocking websites from its broadband customers; in response Virgin have described the problem as a glitch in their network which has been worked around and currently being investigated.
The sites in question are file storage site such as Megaupload and Rapidshare which allow users to upload and store files, these same files can be downloaded by other users.
Accusations that some users have been using the sites to share music and films illegally only add weight to the theory that the websites were blocked on purpose.
One major concern with the Digital Economy bill was that some broadband deals could bock it users from sites deemed to allow access or promote illegal file sharing.
Virgin were quick to release a statement via its Twitter feed denying the blocking.
Virgin was extremely quick to respond and to reiterate that it was down purely to a technical glitch, hoping that it would put to bed any of its customers fears.
Despite solving the initial problem further comments have been made suggesting that speeds on the file storage sites are far below average.
With one customer noting that with a 50 megabyte broadband connection they where only reaching download speeds of around 6 meg. As yet there has been no comment on this but it may be somewhat due to the original technical glitch and the work around Virgin had to implement to allow its customers access to the sites.
In general, it's expected that broadband deals with good broadband fair use policies (that is the most fair ones will be the ones least likely to block).
Some broadband providers have also come out in public as being firmly against blocking websites from their broadband users while others haven't said anything about it as yet.
Some mobile broadband providers are also well-known for blocking certain sites and services.
For example, certain mobile broadband providers who also happen to be mobile phone providers and shall remain nameless (ok, it's t-mobile) only offer VOiP services such as Skype on their more expensive mobile broadband deals.
This means that ordinary mobile broadband customers to this service will find these sites bocked and be unable to use them.
