There's no need to get too bogged down in the legalities of this. A glance at the Communications Act 2003, Section 363, tells all:
http://www.legislation.gov.uk/ukpga/2003/21/section/363
S363- Licence required for use of TV receiver
(1)A television receiver must not be installed or used unless the installation and use of the receiver is authorised by a licence under this Part.
(2)A person who installs or uses a television receiver in contravention of subsection (1) is guilty of an offence.
(3)A person with a television receiver in his possession or under his control who—
(a)intends to install or use it in contravention of subsection (1), or
(b)knows, or has reasonable grounds for believing, that another person intends to install or use it in contravention of that subsection,
is guilty of an offence.
The section goes on to describe the maximum penalty for contravention (£1,000 fine).
This is fairly straightforward, explaining that installation or use of a TV is an offence. It is an Act of Parliament and forms part of criminal law, so contravention is illegal.
The BBC or its agents do not have automatic right of entry but may obtain a warrant, This is dealt with under S366:
http://www.legislation.gov.uk/ukpga/2003/21/section/366
S366 - Powers to enforce TV licensing
(1)If a justice of the peace, a sheriff in Scotland or a lay magistrate in Northern Ireland is satisfied by information on oath that there are reasonable grounds for believing—
(a)that an offence under section 363 has been or is being committed,
(b)that evidence of the commission of the offence is likely to be on premises specified in the information, or in a vehicle so specified, and
(c)that one or more of the conditions set out in subsection (3) is satisfied,
(Subsection 3 sets out a number of conditions where a warrant may be issued, including that where access would be denied without a warrant).
All fairly uncomplicated.