Under The Equality Act 2010 §13(1),
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.
Religion or belief is listed as a protected characteristic under §4. However it is not established that the described characteristic is a "belief" in the relevant legal sense. See Grainger plc and others v Nicholson, which established criteria for deeming an ordinary belief to be a protected belief:
The belief must be genuinely held.
It must be a belief and 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
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.
It is established, then, that belief (ergo disbelief) in man-made climate change is a protected belief. Similarly, ethical veganism (and its denial) is a protected belief (Casamitjana Costa v The League Against Cruel Sports). This article lists as additional established protected beliefs:
Left wing democratic socialism
The sanctity of life, extending to a fervent anti-foxhunting and
anti-hare coursing belief
A genuine and deeply held belief in Scottish independence
A belief in spirituality and the ability of mediums to communicate
with the dead
The “higher purpose” of public service broadcasting in promoting
cultural interchange and social cohesion
Public service and the need to engender in others a desire and
commitment to serve the community for the common good
That it is wrong to lie under any circumstance
The United Kingdom should not be ruled by a hereditary monarch but
should be a democratic and secular republic
Your cited belief is not on the list, but you could try to make law with a test case.
Beyond the determination that something is discrimination, consequences for any part would also have to prove that the discrimination is prohibited. Under the Equality Act §39, for work, that means "An employer (A) must not discriminate against a person (B)", which is to say if Adam and Bob are customers in the lobby, neither party will be sanctioned, nor will they is they are employees of Timmy. So I assume that Bob is Adam's employer.