The largest group in the European parliament has urged the UK government to do the “responsible thing” and extend the Brexit transition period, as coronavirus plays havoc with the timetable for an EU-UK deal.

The centre-right European People’s party (EPP), which unites the parties of 11 EU leaders, including Angela Merkel and Leo Varadkar, issued a statement on Monday calling on the government to extend the Brexit transition beyond the end of the year.

Christophe Hansen, a MEP from Luxembourg who sits on the European parliament’s international trade committee, said: “Under these extraordinary circumstances, I cannot see how the UK government would choose to expose itself to the double whammy of the coronavirus and the exit from the EU single market, which will inevitably add to the disruption, deal or no deal.

“I can only hope that common sense and substance will prevail over ideology. An extension of the transition period is the only responsible thing to do.”

David McAllister, the German MEP who leads the European parliament’s work on the future relationship with the UK, said the pandemic complicated an “already very ambitious” schedule. “The ball is now clearly in the British court,” he added.

Under the withdrawal agreement, the Brexit transition period ends on 31 December 2020, terminating British membership of the EU single market and customs union. But it can be extended for one or two years if both sides agree by 1 July.

The EU has made little secret it would back any extension request, but the British government continues to rule that out.

Responding to the EPP statement, a UK government spokesperson said: “The transition period ends on 31 December 2020, as enshrined in UK law, which the prime minister has made clear he has no intention of changing.”

The plea for extra time comes as British and EU politicians prepared to hold their first meeting to discuss putting in place the Irish Sea border. The Cabinet Office minister, Michael Gove, was due to hold a conference call with the European commission’s vice-president, Maroš Šefčovič, on Monday to discuss how to implement the agreement on the Irish border. The pair were also due to discuss citizens’ rights, amid concern from campaigners that the coronavirus crisis would make it harder for European Union nationals in the UK to secure their status.

Following the meeting, the two sides issued separate statements and each described talks as “constructive”. However, the EU struck a more insistent tone, saying there was an “urgent need” for a timetable on putting into place customs procedures and animal health checks on goods entering Northern Ireland from Great Britain.

EU officials have been alarmed by repeated statements from the prime minister that there will not be controls on goods crossing this internal UK border – a statement that contradicts what he agreed in the withdrawal agreement.

The British government stated it was committed “to upholding our obligations under the Northern Ireland protocol”.

The latest talks were not intended to touch on the future relationship, amid rising doubts about the prospects for agreeing an unprecedented deal spanning trade, security and fishing rights by the end of the year.

British and EU negotiators had concluded only three and a half days of formal talks before the coronavirus struck Europe heavily. A second round due to be held in London earlier this month was scrapped, while next week’s talks seem unlikely to go ahead, despite previous hopes of running them by video conference.

British officials say they continue to explore video-conferencing. But it’s not a simple fix. At least 10 to 20 people can take part in just one thematic topic for each side, making virtual talks complicated to organise when individuals are working from home. Talks may cover about 10 different themes.

The EU’s chief negotiator, Michel Barnier, has the virus, while his UK opposite number, David Frost, has symptoms and has gone into self-isolation. Officials on both sides say they are in regular contact.