A lot of people have talked to me over the last week about Wi-Fi (open and closed, i.e. password-protected) and the Digital Economy bill. The more I try to find answers, the more ludicrous it becomes. For instance, last week it turned out that a pub owner was allegedly fined £8,000 because someone downloaded copyright material over their open Wi-Fi system. Would that get worse or better if the Digital Economy bill passes in its present form?

To illustrate, I'm going to pick my favourite example of a potentially worried wireless network provider: my mum.

She doesn't understand or like the internet, refuses to even think about securing her Wi-Fi network. What is her legal status? What will she say if/when she receives warnings under the Digital Economy bill because someone has used her open Wi-Fi to download infringing files?

Well, the bill contemplates that warnings can be sent only to "subscribers". These include alleged infringers, and those who have "allowed" others to use their access to the internet to allegedly infringe. That sounds a lot like it covers those who operate Wi-Fi networks (and is meant to). Later in the bill, however, a "subscriber" is defined as any person who "(a) receives the service under an agreement between the person and the provider of the service; and (b) does not receive it as a communications provider".

This leaves two avenues of defence for my mum. One: she might say she was a "communications provider" and thus not a subscriber. This is at least arguable under the Communications Act 2003 definition of such, and might get her out of the bill (hurrah). But if my mum is not a poacher, is she a gamekeeper? If not a "subscriber", is she an "internet access provider"? The definition in the bill is that an ISP is someone who provides an "internet access service", itself defined as :

"an electronic communications service that (a) is provided to a subscriber; (b) consists entirely or mainly of the provision of access to the internet; (c) includes the allocation of an IP address or IP addresses to the subscriber to enable that access".

My mum may fit these conditions. (Does she "allocate" an IP address? Who knows? Certainly not my mum.) But is there an "agreement" between her and an unknown Wi-Fi piggybacker? My mum's Wi-Fi has no "I accept" box. "Agreement" is defined nowhere in the bill. But suppose my mum leaves her network unsecured due to ignorance – and the "subscriber"s laptop logs on to the nearest open Wi-Fi network automatically as he sits on the bench outside? In such circumstances, can there truly be "agreement"?

Maybe not, which is good for my mum, but not so good for the government, because it drives a coach and horses through the intention of the bill, which is to ban open Wi-Fi so that it cannot be used as an excuse when (whenever that is) the opportunity comes to repel the unfounded allegations of infringement which generate the warnings. (How my mum could even start to know how to do this without legal aid – which will clearly not be available – is beyond me – but let's leave that for now too.)

A hardened contract lawyer will already be muttering that in English law formation of contract is an objective not subjective matter. If my mum appears to extend a service of internet access, and a downloader appears to accept it, does it matter what they actually think? Isn't this objectively an "agreement"? The Department of Business, Innovation and Skills (DBIS), which is pushing the Digital Economy bill through, would probably like this argument, at least on first thoughts, because it plugs the gaps in the enforcement scheme. But it has big problems of its own. My mum would not be a subscriber, but she would be deemed an "ISP", which would mean she would be bound to comply with sending out of warnings to those users of her service whose IP addresses were passed to her by rightsholders, or else, er, face up to a £250,000 fine for non cooperation.

Even DBIS may grind to a halt at this point. Not only is fining grannies a quarter of a million pounds for not being hip with the internet not going to go down well in Daily Mail land, but it would be impossible for my mum to pass the warnings on: although she may have unknowingly "allocated" her IP address to the "subscriber", she has no way of identifying those who have used her Wi-Fi, and no way to pass those warnings – and the legal responsibility - on.

Let's try a different example. My mum is a dinosaur, let us say. She will be re-educated and her consciousness raised in the great Mandelson Digital Britain future. But the DEB is meant to be a business-friendly piece of legislation so presumably it will work fine for businesses – or will it? Let's think about a big solid business, like McDonalds. McDonalds have a nice well run, password protected Wi-Fi network.

So do many public institutions, like the venerable British Library, which likes to assist scholars and patrons by providing such facilities. In both cases, the Wi-Fi supplier will probably be regarded as a communications provider and hence not a subscriber. In both cases, it is very easy to see this time that an "agreement" is explicitly made between the Wi-Fi service and the recipient.

What happens this time if a passing user logs on, downloads infringing material and a warning is dispatched? McDonalds may cope because its Wi-Fi is provided by The Cloud, which can possibly cope with identifying which user is to get which warnings. It will be fiddly and expensive though and the cost of Wi-Fi to McDonalds would probably go up so much it would be uneconomic to supply. Bang goes a free service which has proved a public boon and a remarkably popular enticement to customers in the ongoing recession.

But if we turn to the British Library, it really bites. The BL is not set up to be a forensic investigator; obliging it to act as one will be a fantastically resource intensive exercise for a public body providing a free service. There is also an issue of privacy and anonymity, something academic researchers are often touchy about. And again, if the BL refuse to comply – or more likely, simply says it can't – it is, at least in theory, subject to a fine up to £250,000.

So we are back again to the death of public Wi-Fi, closed as well as open. Can anyone disprove this train of logic? Because really, I may be a lawyer, but I don't like it any more than you do.

Lilian Edwards is professor of internet law at Sheffield University

Update: corrected - British Library is not open (caption); pub being fined is "alleged" as it would have been civil damages; corrected © to (c) [error introduced by autocorrecting word processor]; minor grammar.