Britain would not be able to rejoin the EU on the special terms it enjoyed in the past, veterans of the Brexit negotiations have said.

According to former officials from around Europe, the UK should not expect to achieve as beneficial a deal as it once had if it decided to begin negotiations on re-entry.

The warnings came as senior Labour politicians jostling for the leadership of their party and country talk openly about wanting to return to the union at some point in the future.

Georg Riekeles, a former adviser on the EU’s Brexit taskforce, said he expected member states would take “a very warm, welcoming” stance but also a “hard-headed” one to a British membership application.

“There is a strategic need for the EU and the UK to work together, but I don’t think there would be an appetite for opening up new decades of British exceptionalism,” he said. “The price of re-entry would be membership on normal terms.”

During its 47 years of EU membership, the UK achieved an unprecedented special status: opt-outs from core policies, such as the single currency and the Schengen passport-free zone, as well as a rebate on EU budget payments, while carving out an agenda-setting role.

Sandro Gozi, Italy’s Europe minister from 2014-18, said “certainly we will start” with those standard terms, when asked about the euro and Schengen zone membership in any re-entry negotiations. “It is clear that the tailor-made suit is gone, and it is clear that the negotiation of the UK should tackle all the issues which are foreseen for any candidate.”

Gozi, now an MEP and chair of the European parliament’s delegation to the EU-UK parliamentary partnership assembly, predicted EU member states would welcome a British application to rejoin despite the uncertainty of a possible Nigel Farage premiership.

Wes Streeting argued over the weekend that the UK should rejoin the EU in the future. Even though the former health secretary’s allies say this could not happen without an election or referendum to gain permission from British voters, his comments reignited long-dormant rifts over Europe at the top of the ruling Labour party.

Andy Burnham, the Greater Manchester mayor, who is seeking a return to Westminster to challenge the prime minister, has previously said he wants Britain to rejoin the bloc within his lifetime. However, on Monday he clarified that he would not try to make that happen if he became prime minister in the short term.

“[Brexit] has been a major disaster for the UK, but it has also been a loss for the EU … If in a moment of such a huge global turmoil, the UK decided to ask to rejoin the EU, I think that for our political model it would be a great victory.” He stressed this was not a victory over the UK but about its “attractiveness”.

Britain, he said, had other options, such as “being associated with the single market” and being a founder of a new European security council, a proposed defence leadership body that could involve up to a dozen members, but has yet to be fully detailed. “I think that the options are more than simply the full accession. But that would be very much up to the UK to make up their mind, to understand what they want,” he said.

Poland’s anglophile foreign minister, Radosław Sikorski, has also warned Britain not to expect a similar deal to its “de-facto à la carte membership” of the past. British elites, he said earlier this month, needed to “internalise” the fundamental European deal “that you get more benefits in return for pooling of some aspects of sovereignty”.

An application from the UK – a former member that went through a bitter divorce – was also regarded as unlike any other.

Riekeles, now an associate director at the European Policy Centre, said many in European capitals and Brussels were welcoming “the spirit and signals” from the UK but stressed this was a long way from a formal process. “The EU would need to see a durable national consensus that the UK has really changed its mind.”

Reflecting on his own experience, he said: “The EU can work with a UK that knows what it wants. It struggles with a UK that wants the benefits of integration while keeping the politics of separation.”

“The world of Brexit is gone,” he said alluding to Russian militarism, Chinese economic coercion and Donald Trump’s “America first” policy. “I think everybody with their full senses should see that the UK and the EU are part of the same strategic space. If this was the national consensus [for the UK to rejoin] … I think the EU would engage all in, very seriously. But are we there now? Not yet.”

The European Commission’s chief spokesperson, Paula Pinho, declined to comment on potential negotiating terms. Referring to an upcoming EU-UK summit, widely expected in early July, she said: “There are discussions on closer cooperation on a number of areas. That is where we are and that is also what we are doing, precisely in preparation of the next summit, rather than speculating about big, new or renewed issues.”