Next year we anticipate that regulations will come into force which provide for legal deposit for non-print works, mirroring the longstanding situation for printed works. The final draft of the regulations, to be laid before Parliament, has recently been published.
Here's a summary of their impact in relation to web archiving.

What will we be collecting ?

The regulations cover four deposit models, of which the most relevant for the web archiving team are that:

(i) a deposit library may copy UK publications from the open web, including  websites, plus open access journals and books, government publications etc.;
(ii) a deposit library may collect other password-protected material by harvesting, subject to giving at least 1 month’s written notice for the publisher to provide access credentials (with some limited exemptions).

The regulations apply to any digital or other non-print publication, except:

(i) film and recorded sound where the audio-visual content predominates [but, for example, web pages containing video clips alongside text or images are within scope];
(ii) private intranets and emails;
(iii) personal data in social networking sites or that are only available to restricted groups.

The regulations apply to online publications:

(i) that are issued from a .uk or other UK geographic top-level domain, or;
(ii) where part of the publishing process takes place in the UK;
(iii) but excluding any which are only accessible to audiences outside the UK.

What will the Library be able to do with it ?

Deposited material may not be used for at least seven days after it is deposited or harvested.

After that, deposit libraries may:

(i) transfer, lend, copy and share deposited material with each other;
(ii) use deposited material for their own research;
(iii) copy deposited material, including in different formats, for preservation.

What will users be able to do with it ?

Users may only access deposited material while on “library premises controlled by a deposit library”.

Users may only print one copy of a restricted amount of any deposited material, for non-commercial research or other defined ‘fair dealing’ purposes such as court proceedings, statutory enquiry, criticism and review or journalism.

No more than one user in each deposit library may access the same material at the same time.

Users may not make any digital copies, except by specific and explicit licence of the publisher.

What restrictions may publishers request ?

The publisher or other rights holders may request at any time an embargo of up to 3 years, and may renew such request as many times as necessary. The requested embargo must be granted if the deposit library is satisfied on reasonable grounds that providing access would conflict with the publisher’s or rights holders’ normal exploitation of the work and unreasonably prejudice the legitimate interests of the publisher.

These conditions remain in force forever, including after all intellectual property rights in the deposited material have expired [“perpetual copyright”].