Is it legal to film inside of a venue such as a bar or nightclub? The film would be used for marketing material for a business.
'Is it legal?' could mean one of two things.
Does it break the criminal law; could I be arrested?
There is no law criminalising photography or filming in a private place (assuming you're not doing something amounting to harrassment, or making something inherently illegal like child pornography). The act of filming per se is therefore not illegal in a criminal sense. However, the proprietor of a private place can ask you to stop filming or demand that you leave; if you fail to comply then you will be trespassing.
Trespass is not a criminal offence (although the police will undoubtedly remove you if called). However, if your intent was to intimidate, obstruct or disrupt activity within the premises, you could be charged with Aggravated Trespass under s68 Criminal Justice and Public Order Act 1994.
Could the owner, or someone else, have a civil claim against me?
This is more difficult to answer. Trespass is a tort, so the owner could in theory have a claim against you if you were filming against his wishes. However, he would have to prove some measurable amount of damage, and this is why few trespass cases come to court.
The occupants of the premises may be able to sue if you breach their right to privacy (Article 8 ECHR, incorporated into UK law by the Human Rights Act 1998); however, a court will balance this against your Article 10 right to freedom of expression. A court will consider all circumstances: for example, if you were filming in the toilets of a nightclub, the occupants' right to privacy may well outweigh your right to freedom of expression.
A copyright owner may have a claim against you if you include their work in your film; for example, if you film inside a nightclub and substantial parts of songs are captured on your film, this may give rise to a claim.
I am not a lawyer. Don't rely on free advice from strangers on the Internet.
Unrelated but corollary: I have walked into venues in the United States where a sign had been posted on the door stating
"Filming is occurring on these premises from dates XX-YY during the hours HHHH. By entering you are consenting to this filming. If you prefer not, we look forward to your business again on YYYY-MM-DD"
I do not know the legal efficacy (binding ability) of this kind of 'contract.' Certainly, you are subject to certain terms on private properties, which you implicitly accept.
It is lawful but if you are asked to leave the premises then you must do so immediately. They also have the right to ban you from returning to the premises, if they do then you must not re-enter the premises. However it is inadvisable unless you have permission, preferably in writing. Especially for business use.