Can a member of the public be denied access to a public place during an "officially authorised" event?
In England and Wales - Yes
A person's freedom of movement at public assemblies may be restricted by the imposition of conditions described at s.14 of the Public Order Act 1986...
(1) If the senior police officer, having regard to the time or place
at which and the circumstances in which any public assembly is being
held or is intended to be held, reasonably believes that—
(a) it may result in serious public disorder, serious damage to
property or serious disruption to the life of the community, or
(b) the purpose of the persons organising it is the intimidation of
others with a view to compelling them not to do an act they have a
right to do, or to do an act they have a right not to do,
he may give directions imposing on the persons organising or taking
part in the assembly such conditions as to the place at which the
assembly may be (or continue to be) held, its maximum duration, or the
maximum number of persons who may constitute it, as appear to him
necessary to prevent such disorder, damage, disruption or
intimidation.
(2) In subsection (1) “the senior police officer” means—
(a) in relation to an assembly being held, the most senior in rank of
the police officers present at the scene, and
(b) in relation to an assembly intended to be held, the chief officer
of police.
(3) A direction given by a chief officer of police by virtue of
subsection (2)(b) shall be given in writing.
(4) A person who organises a public assembly and knowingly fails to
comply with a condition imposed under this section is guilty of an
offence, but it is a defence for him to prove that the failure arose
from circumstances beyond his control.
(5) A person who takes part in a public assembly and knowingly fails
to comply with a condition imposed under this section is guilty of an
offence, but it is a defence for him to prove that the failure arose
from circumstances beyond his control.
(6) A person who incites another to commit an offence under subsection
(5) is guilty of an offence.
(7) [Repealled]
(8) A person guilty of an offence under subsection (4) is liable on
summary conviction to imprisonment for a term not exceeding 3 months
or a fine not exceeding level 4 on the standard scale or both.
(9) A person guilty of an offence under subsection (5) is liable on
summary conviction to a fine not exceeding level 3 on the standard
scale.
(10) A person guilty of an offence under subsection (6) is liable on
summary conviction to imprisonment for a term not exceeding 3 months
or a fine not exceeding level 4 on the standard scale or both.
https://www.legislation.gov.uk/ukpga/1986/64/section/14?timeline=false
Note that even if s.14 is not engaged for whatever reason, the police have a number of powers to prevent (and deal with) public disorder, breaches of the peace etc.
Also note that there is no requirement to inform the authorities if the rally is "static", however the organisers of parades or marches must inform the police 6 days in advance and s.12 of the 1986 Act details similar provisions as above.
https://www.gov.uk/protests-and-marches-letting-the-police-know
https://www.legislation.gov.uk/ukpga/1986/64/section/12?timeline=false