Mr Johal, detained in India since 2017 on accusations of involvement with a banned Sikh separatist group, denies wrongdoing and a UN panel ruled his detention "arbitrary".
His family alleges he has been tortured and, despite being acquitted in one case, he still faces multiple federal charges which his legal team describes as "Kafkaesque".
Mr Johal's brother, Gurpreet Singh Johal, believes Starmer is well-placed to secure his release, citing recent high-profile releases of other Britons detained abroad.
A tort claim against the UK government, alleging British intelligence services contributed to Mr Johal's arrest and torture, began in court this week.