Paul Black, who suffers from a range of serious health problems, has taken his case to the Supreme Court in a bid to win what he says is the same level of protection from the risks posed by passive smoking as "non-smokers living in the wider community".
Tuesday's proceedings in London before a panel of five justices, headed by the court's president Lady Hale, follow his defeat at the Court of Appeal last year.
The case centres on the 2006 Health Act which places restrictions on smoking in public places and workplaces, making it a criminal offence to smoke in an unauthorised place and also an offence for those in charge of the premises to turn a blind eye to the smoking.
Black, an inmate at HMP Wymott in Lancashire, originally won a High Court declaration in 2015 that the legal ban on smoking in public places under that Act must also be applied to state prisons and other Crown premises in England and Wales.
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But appeal judges later allowed a Government challenge against that decision, ruling that the Crown was not bound by the Act and the ban, which came into force in July 2007, did not apply in public sector prisons.
The Supreme Court is now being asked to decide whether the Court of Appeal reached the correct findings.
Black, a sex offender serving an indeterminate sentence, launched his legal action complaining that prison smoking rules were being flouted and should be legally enforceable.
He argues that he and other prisoners should have confidential and anonymous access to the NHS Smoke-Free Compliance line which enables members of the public to report breaches of the law to the local authority.
The Justice Secretary has refused his request, contending it would serve no purpose since the Act does not bind the Crown - meaning that a local authority could play no role in enforcing the ban in the state-run prison.
Philip Havers QC, for Black, told the justices: "It is submitted that it is clear from the terms of the legislation itself that Parliament intended the Crown to be bound by the smoking ban."
He argued that if the Act does not bind the Crown "then it is not only the vast majority of prisoners who will be deprived of the protection of the Act, but also all those other persons who work in or visit all other Crown premises".
Visitors would include children "who are particularly at risk from passive smoking".
A Prison Service spokeswoman said: "We have long been committed to a smoke-free prison estate and this is being phased in over a long period of time.
"This phased introduction will reduce the risk to staff and prisoners of exposure to second hand smoke and prisons will only become smoke-free when it is appropriate to do so."