Boris Johnson has been criticised for congratulating Viktor Orban on his re-election as Hungary's prime minister.
The nationalist leader and his Fidesz party had secured a resounding victory in Sunday's vote.
However, opposition politicians branded Mr Johnson's wishes for an "authoritarian leader" as "hugely inappropriate", claiming he had "embarrassed" the UK Government.
Campaign groups also expressed concern about "anti-Semitic undertones" to Mr Orban's campaign, the Hungarian leader's comments about Muslims, and the politician's attitude towards refugees and migrants.
Meanwhile, international observers to Hungary's election highlighted a "pervasive overlap between state and ruling party resources, undermining contestants' ability to compete on an equal basis".
The Organisation for Security and Co-operation in Europe (OSCE) said: "Voters had a wide range of political options, but intimidating and xenophobic rhetoric, media bias and opaque campaign financing constricted the space for genuine political debate, hindering voters' ability to make a fully informed choice."
Posting on Twitter on Monday, Mr Johnson wrote: "Congratulations to Fidesz and Viktor Orban on winning the elections in Hungary.
"We look forward to working with our Hungarian friends to further develop our close partnership."
Asked later on a trip to Sweden whether she had congratulated Mr Orban on his re-election, Prime Minister Theresa May appeared to offer a more luke warm assessment of the result.
She said: "The UK has a history of many years of cooperation with the Hungarians and we look forward to continuing to work with the Hungarian government in the future."
Mr Johnson was joined in congratulating Mr Orban by European Council President Donald Tusk, although the EU boss also added: "During your renewed term as Prime Minister I count on you to play a constructive role in maintaining our unity in the EU."
As a strong eurosceptic, Mr Orban has frequently clashed with Brussels over attempts to force EU member states to take in quotas of refugees.
Following Hungary's election, former UKIP leader Nigel Farage praised Mr Orban as "the strongest leader in Europe and the EU's biggest nightmare".
France's National Front leader Marine Le Pen praised Mr Orban's "great and clear victory", while the Netherlands' anti-Islam politician Geert Wilders hailed the "excellent result".
Responding to the Foreign Secretary's congratulations for Hungary's prime minister, Labour's shadow foreign minister Fabian Hamilton said: "Given the already damning reports from international bodies on how this election was conducted, it seems hugely inappropriate for Boris Johnson to congratulate Viktor Orban on winning it."
Mr Hamilton added it was "disgraceful" Mr Johnson failed to mention the Hungarian government's "shameful record on political freedom, women's equality and LGBT rights" or Mr Orban's "Islamophobic rhetoric" or "anti-Semitic attacks" on Hungarian-American billionaire George Soros.
Mr Soros's philanthropy for his refugee charity became a frequent target for Mr Orban during his election campaign.
Jo Swinson, the Liberal Democrats' deputy leader, claimed Mr Johnson had "embarrassed the Government" on the same day the OSCE had criticised Mr Orban's re-election.
She said: "We would expect the Foreign Secretary to take these allegations more seriously and work with colleagues across Europe to investigate whether the election in Hungary was fair."
The SNP's Stewart McDonald branded Mr Johnson's congratulations for the Hungarian leader "shameful", while Labour MP Peter Kyle, a supporter of the pro-EU Open Britain campaign, said: "It seems there's not a single authoritarian leader Boris Johnson won't pander to in pursuit of his hard Brexit fantasy. Viktor Orban in Hungary is just the latest.
"This is all eerily reminiscent of the Boris Johnson's shameless sucking up to Donald Trump.
"It demeans our country and it's not worthy of his position as Foreign Secretary."
Meanwhile, the Board of Deputies for British Jews expressed concern at the "anti-Semitic undertones" of Mr Orban's campaign against Mr Soros, and the use of "classic anti-Jewish tropes" in his description of opponents.
The organisation also condemned Mr Orban's comments about "Muslim invaders" and description of migrants as "a poison".
Amnesty International warned against "attempts to stoke hostility towards refugees and migrants" under Mr Orban.
The Hungarian Prime Minister's victory also sparked a row in the European Parliament.
German MEP Manfred Weber, the chair of the European People's Party (EPP) group in the European Parliament, was challenged for offering his congratulations to Mr Orban by Guy Verhofstadt, the European Parliament's Brexit coordinator.
Mr Orban's Fidesz party is a member of the EPP, which is led by European Commission president Jean-Claude Juncker.