This judgment is of historic interest only as the right of appeal under consideration by the court was re-written by the Immigration Act 2014 anyway. For what it is worth, the old section 83 did not give a right of appeal against refusal of asylum to a person who already had leave at the time that the person applied for and was refused asylum. Under the new, current appeal regime a refusal of asylum always now generates a right of appeal.
From the useful Supreme Court press summary:
BACKGROUND TO THE APPEAL
This case concerns the statutory rights to appeal immigration decisions under the Nationality, Immigration and Asylum Act 2002 (“NIAA 2002”). The relevant provisions have now been repealed, however they were relevant to the appellant because of the timing of his claim. The main right of appeal under NIAA 2002 in relation to immigration decisions was s82. Whilst this did not cover asylum claims, where an appeal existed under s82 then the claimant in question was entitled by s84(1)(g) to raise the argument that his removal would put the UK in breach of its obligations under the Refugee Convention. By this route, a right of appeal against refusal of asylum effectively existed in NIAA 2002 if there was an immigration decision to appeal under s82. Generally there was such a decision to appeal under but not in all circumstances. For example, where the asylum was refused but leave to remain was granted. In this context, s83 provided a specific, additional right of appeal against refusal of asylum where the asylum claim was rejected but the applicant had, per s83(1)(b), “been granted leave to remain or enter the [UK] for a period exceeding one year (or for periods exceeding one year in aggregate)”.
The appellant is a citizen of Uganda. On 27 September 2010, he was granted limited leave to remain in the United Kingdom as a student until 30 April 2012. Before that time had expired, on 7 February 2012, he applied for asylum on the grounds that the Ugandan government’s treatment of him might be affected because of his family’s alleged political activities in Uganda. The Secretary of State rejected his claim and did not vary his limited leave to remain. The question was whether under s83 it was necessary for the relevant grant of leave to remain to be contemporaneous with or to post-date the refusal of the asylum claim in order for the appellant to benefit from the right of appeal. After being unsuccessful before the Court of Appeal the appellant appealed to the Supreme Court.
The Supreme Court unanimously dismisses the appellant’s appeal. Lord Hughes gives the only judgment, with which the other Justices agree.
REASONS FOR THE JUDGMENT
Lord Hughes identifies four possible readings of s83: 
- any grant(s) of leave to remain totalling more than 12 months bring the claimant within the section, whenever they occurred and whether or not they had expired before the asylum claim was made and determined;
- grant(s) of leave to remain totalling more than 12 months bring the claimant within the section providing such leave is still current at the time of the determination of the asylum claim;
- grant(s) of leave to remain bring the claimant within the section providing that such leave totalled more than 12 months counting from the date of refusal or later grant, and whether the grant(s) were made before or after refusal.
- grant(s) of leave to remain totalling more than 12 months bring the claimant within the section if but only if they (and all of them if more than one) are either contemporaneous with or post- date the determination of the asylum claim; this was the Secretary of State’s primary case and was adopted by the Upper Tribunal and the Court of Appeal.
Lord Hughes notes that whilst s83 can be read as a matter of language a number of ways, some are more natural than others. In particular, s83 appears to focus on the time when the asylum claim has been rejected, for it is concerned with appeals against this decision, and then to ask whether, when a claimant wishes to appeal, the condition in subsection 1(b) is met. 
The purpose of s83 is tolerably clear. It is to provide an additional and more targeted right of appeal beyond the ordinary one created by s82. It is to provide a vehicle for the determination by the tribunal of refugee status, when that status is asserted but rejected by the Secretary of State, in those cases where no such vehicle otherwise exists, nor will exist within a reasonable time. s83 was designed to create an extra right of appeal for those who have a longer period of leave to remain and who would otherwise have no s82 vehicle which they could use. The intention was that those in this situation should not be deprived of the right to challenge the refusal of their asylum claim where that refusal is not accompanied by a decision to remove them. 
Once this is understood, it is clear that the construction which most neatly serves the purpose of the statute is interpretation “3”, i.e. that grants of leave to remain bring the claimant within the section providing that such leave totalled more than 12 months counting from the date of refusal or later grant, and whether the grants were made before or after refusal.