It might be unlawful. As noted in other answers, the general rule is that a business is free to serve or not serve customers as it wishes. This general rule is subject to various exceptions. E.g. laws relating to the specific service (e.g. utilities), contractual obligations, and unlawful discrimination laws. In the case of a negative review, refusal of service could be unlawful discrimination if the circumstances are right.
The relevant provisions of the Equality Act 2010 are:
- Section 4 provides that "religion or belief" is a protected characteristic.
- Section 13(1) defines direct discrimination as: "A person (A) discriminates against another (B) if, because of a protected characteristic, A treats B less favourably than A treats or would treat others."
- Section 29(1) provides that "A person (a “service-provider”) concerned with the provision of a service to the public or a section of the public (for payment or not) must not discriminate against a person requiring the service by not providing the person with the service."
In Grainger plc and others v Nicholson  IRLR 4 (EAT), the Employment Appeal Tribunal set out the following criteria which must be met for something to qualify as a "belief" under the Act:
- The belief must be genuinely held.
- It must be a belief, not an opinion or viewpoint based on the present state of information available.
- It must be a belief as to a weighty and substantial aspect of human life and behaviour.
- It must attain a certain level of cogency, seriousness, cohesion and importance.
- It must be worthy of respect in a democratic society, not be incompatible with human dignity and not conflict with the fundamental rights of others.
So, the answer may well depend on the content of the review and the motivation in posting it. A review that you think "the manager is always a mean jerk to everyone" probably fails at least the 2nd and 3rd criteria. On the other hand, in Casamitjana Costa v League Against Cruel Sports ET/3331129/18, an employment tribunal held that veganism could meet the criteria. Thus, a review posted by someone with a genuine belief in veganism, complaining about a restaurant's meat and dairy practices, could fall within scope. Even then, for the discrimination to be unlawful you would have to establish that the refusal of service was "because of a protected characteristic" (see Section 31(1) above) i.e. that it was because of the vegan views expressed in the review as opposed to because of the fact that a negative review was posted per se. These things can be tricky to prove in court.