The Digital Economy Act itself (the Age Verification bits are in part 3)
Explanatory notes to that act.  Included at the end of these are links to the various debates and committee stages in Parliament.

The regulations about commercial providers. The link is to the draft regulations but they were approved by Parliament on December 17th.

BBFC guidance which includes

Guidance on Age-verification Arrangements

Guidance on Ancillary Service Providers

And Memorandums of Understanding with the Information Commissioner and Internet Watch Foundation.

The debate in Parliament when these were approved was on December 17th

The government’s web page includes further government documents about the act including the guidance issued to the Age Verification Regulator and impact assessments.

Several parts of the legislation came into force on 31st July 2018 in the Commencement Order No 1.  Other commencement orders have been made for other parts of the act and at the time of writing (22nd Dec 2018) the other parts of the Age Verification Legislation are awaiting commencement orders.

Other legislation

Criminal Justice and Immigration Act 2008 (the legislation on extreme pornography)

CPS charging guidance relating to Extreme Pornography offences

Legislation is linked to latest version on legislation.gov.uk which may not be up to date with latest amendments.