The copyright clauses which are added as additional sections of the Communications Act 2003 all refer to internet service providers and subscribers.
These are defined as follows:
“internet access service” means an electronic communications service that—
(a) is provided to a subscriber;
(b) consists entirely or mainly of the provision of access to the internet; and
(c) includes the allocation of an IP address or IP addresses to the subscriber to enable that access;
“internet service provider” means a person who provides an internet access service;
“IP address” means an internet protocol address;
“subscriber”, in relation to an internet access service, means a 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;
It is the (b) associated with "Subscriber" that is the most interesting. If we go to section 405 of the Communications Act 2003 we find:
“communications provider” means a person who (within the meaning of section 32(4)) provides an electronic communications network or an electronic communications service
“electronic communications network” and “electronic communications service” have the meanings given by section 32Going to section 32 brings us:
(1) In this Act “electronic communications network” means—
(a) a transmission system for the conveyance, by the use of electrical, magnetic or electro-magnetic energy, of signals of any description; and
(b) such of the following as are used, by the person providing the system and in association with it, for the conveyance of the signals—
(i) apparatus comprised in the system;
(ii) apparatus used for the switching or routing of the signals; and
(iii) software and stored data.
(4) In this Act—
(a) references to the provision of an electronic communications network include references to its establishment, maintenance or operation;
(b) references, where one or more persons are employed or engaged to provide the network or service under the direction or control of another person, to the person by whom an electronic communications network or electronic communications service is provided are confined to references to that other person; and
(c) references, where one or more persons are employed or engaged to make facilities available under the direction or control of another person, to the person by whom any associated facilities are made available are confined to references to that other person.
My reading of this is that if you tell your ISP that you will be installing your own router ("apparatus used for the switching or routing of the signals") and that you will be managing it yourself ("establishment, maintenance or operation") then you classify as a Communications Provider under the bill and they are then not liable to respond to any reports sent from copyright owners that are related to your IP address.