Lord Alton and MP Fiona Bruce (both pictured above) said also warned the move might contravene an international UN treaty which protects someone from being punished more than once for the same crime.
The pair signed a letter in the Guardian which said: "[The] verdict is not only outrageously unjust because these three young men had already served their sentences and because it strikes a severe blow to Hong Kong's freedoms..."
The High Court sentenced Joshua Wong (20), Alex Chow (27) and Nathan Law (24) on Thursday to six, seven and eight months in prison respectively.
Following a decision by the Hong Kong government to re-open the case, judges over-turned an earlier verdict. They agreed with prosecutors that previous non-custodial sentences were too lenient.
Last year, Joshua Wong and Nathan Law both served community service, while Alex Chow received a three-week suspended prison sentence.
They were punished for leading or encouraging an illegal rally in September 2014 against plans by Beijing to restrict elections.
The demonstration led to the so-called Umbrella Movement, which saw major streets brought to a standstill for eleven weeks.
The latest court decision has been interpreted as a further indicator tolerance of dissenting voices in the Chinese-governor territory is waning.
The letter appearing in the Guardian on Saturday was signed by 23 public figures, including Grover Joseph Rees, the retired United States ambassador.
It said: "As former heads of government, parliamentarians, lawyers and civil society leaders, we stand in solidarity with these three brave young men, we condemn yesterday's verdict by the court of appeal, we call for it to be reviewed and for these three political prisoners to be released, and we urge the international community to put pressure on the governments of the People's Republic of China and the Hong Kong Special Administrative Region to respect the principles of "one country, two systems - and the Basic Law in Hong Kong.
"Joshua Wong, Alex Chow and Nathan Law should be honoured, encouraged and supported, not jailed. Yesterday was a dark day for Hong Kong and it should be met with international condemnation."
Top picture: Nathan Law, Joshua Wong and Alex Chow.