Some of the usual stereotyping of people claiming benefits going on in this thread. Yes, there are some wastrels who opt to live permanently on benefits and by a combination of large families and illegal additions to their incomes manage to have a better than poor living standard. Most people however who are on benefits are in pretty desperate shape. It also isn't really fair to pass comments on people on benefits for having a modern TV - there's precious little else to do for many people, for whom there are few jobs and little money. Getting broadband is still an additional cost in many locations and is also often credit checked, ruling out many claimants from even applying for one.
Eventually access to the internet will be seen as a social service and a free, lower quality service will be provided via public subsidy. Perhaps it will go to streets in poorer neighbourhoods and then be plumbed to houses using a cheaper installation method.
The internet supply market in the UK is heavily distorted - BT are overwhelmingly dominant and this is promoted by the government's rural broadband scheme, for which only BT is used, plus other hidden subsidies over the years. The fact is that BT could already afford to provide heavily subsidised landline/broadband services to claimants and this would probably cost the taxpayer a lot less than the web access provided by work programme companies acting for the DWP.
That said, there are relatively few families now with absolutely no access to any web resources, given the abundance of smart phones and their widespread use even amongst claimants.