The Polish foreign minister believes David Cameron has "fucked up" his handling of the EU by resorting to "stupid propaganda" to appease Eurosceptics, according to an expletive-laden transcript of secretly taped conversations.

Radoslaw Sikorski, who is close to many senior Tories and as an Oxford University student was a member of the Bullingdon Club at the same time as Boris Johnson, made the comments in a conversation with the former Polish finance minister Jacek Rostowski.

The conversation between the two men, printed in Monday's edition of Wprost news magazine, reveals the extent of the fallout between Poland and the UK over Cameron's proposals to change EU migrants' access to benefits.

Downing Street responded to the leaked Polish tapes by saying that the prime minister would continue to stand up for British interests and deal with the "abuse" of free movement because support for the EU in Britain is "wafer thin".

In another secretly taped conversation, the spokesman for the Polish prime minister, Donald Tusk, claims Tusk "fucked him [Cameron] up good" during a conversation with the British prime minister over plans to curb access to benefits in the UK.

In the first conversation, Rostowski, who resigned as finance minister in November, is quoted as saying that "no Polish government could agree" to Cameron's renegotiation proposals, "except in return for a mountain of gold".

It is unclear from the transcript whether the two ministers were discussing Britain's proposed revision of the principles of free movement within the EU, or more specifically the plans to curb EU migrants' access to benefits. It is thought the conversation was taped in spring this year.

Sikorski replies: "It's either a very badly thought through move, or, not for the first time, a kind of incompetence in European affairs. Remember? He fucked up the fiscal pact. He fucked it up. Simple as that. He is not interested, he does not get it, he believes in the stupid propaganda, he stupidly tries to play the system."

To which Rostowski says: "His [Cameron's] problem is that, is that isn't his objective, just a short-term propaganda effect."

Sikorski is quoted as criticising what he sees as the British leader's attempt to appease British Eurosceptics with soundbites: "You know, his whole strategy of feeding them scraps in order to satisfy them is just as I predicted, turning against him; he should have said, fuck off, tried to convince people and isolate [the sceptics]. But he ceded the field to those that are now embarrassing him."

The politicians voice their concerns about Britain leaving the EU, with Rostowski saying that a "Brexit" would be "not especially good for us, generally bad for us, because we would like for Great Britain to stay. I think it'll be the case that [Cameron] will lose the elections. Great Britain will leave."

He then appears to imply that he believes Britain will keep its borders open to EU migration: "Once they do, they'll keep open borders. Not for beggars […] in the sense that they won't let in Gypsy beggars."

Both Sikorski and Rostowski are the most Anglophile of Polish politicians, although Sikorski has become a caustic critic of Cameron's EU policies. Both men were raised and educated in Britain, Rostowski attending Westminster public school and Sikorski studying at Oxford where he was a contemporary of Johnson, Cameron and George Osborne.

The transcripts include a conversation between Pawl Gras, the Polish prime minister's spokesperson, and Jacek Krawiec, the director of Poland's largest oil company, Polish Orlen. The two men appear to be discussing Tusk's fallout with Cameron over the latter's proposals to curb access to benefits: "What the fuck are they on about with these benefits?" Krawiec is quoted as saying. "[Cameron] seems really sensible, I met him at the European forum of new ideas, he chats a lot of sense."

Gras describes Cameron's proposal as "thoughtless", "probably suggested by [some spin doctor] probably came from some focus group", and that the British prime minister "didn't think through the consequences".

"The whole thing was stupid, Donald called him at once to discuss it, he had such a go at him, I mean, fuck, it's a shame we didn't record it, he fucked him up good, had such a proper fucking go at him." "Good," Krawiec responds, "he was right to."

The prime minister's spokeswoman said: "On the broader issue the prime minister has been very clear that support for the EU in the UK is wafer thin. There is real disillusionment amongst British voters about the EU. We need to look at how we reform the EU so that it better focuses the issues people care about – growth and jobs – and addresses and confronts some of the challenges there are.

"Clearly abuse of the right to free movement is one of those issues where people have concerns and where we think it is absolutely right to have a discussion and look at what can be done."

The No 10 spokeswoman denied that the prime minister was wrong to have alienated one of Britain's historic European allies. "If you look around the European council table there are a lot of member states that have strong relations with Britain, where Britain has played an important role in their history. It is for each national leader to stand up for what they believe is in their country's interests and to be prepared to fight for their interests.

"That is exactly what the prime minister is doing when he makes clear, whether it is on the process for appointing the commission president or the need to tackle the abuse of free movement. That is in Britain's national interests and he will fight for that."

Wprost magazine has, over the last week, been publishing transcripts of conversations between high-ranking politicians, leading to speculation that they may force the resignation of Tusk. Wprost has so far refused to say who bugged the conversations or how it obtained the recordings.

Tusk said on Monday that he would not allow his political actions to be dictated by the people behind these "criminal" actions, while Sikorski said his government had been "attacked by an organised criminal group".

Despite the Polish politicians' disparagement of Cameron's policies, an EU summit later this week looks likely to sound accommodating towards his campaign to curb social security benefits for newcomers. A four-page policy paper for the next five-year European commission, drafted by Herman Van Rompuy, the European council president who chairs this week's summit, echoes Cameron's criticisms by saying that public trust in national welfare systems is being eroded by perceived abuses.

The document, obtained by the Guardian, calls on the EU to "guarantee fairness and preserve trust by protecting the achievement of free movement of EU citizens from frauds and abuses which, though limited, affect trust in member states' welfare systems and hinder citizens whose mobility contributes positively to thriving economies."

As the five-year political season gets under way in the EU, there are further moves afoot to counteract high unemployment by cracking down on immigrants. A policy platform being unveiled on Tuesday by the biggest caucus in the new European parliament, the Christian Democrats or European People's party, calls for discrimination against non-EU citizens in the jobs market.

"Member states should give priority in labour market access to EU citizens," says the document, obtained by the Guardian. "We can't just go on as previously in Europe," said Manfred Weber, the new head of the EPP in the parliament. "We need a real reform agenda."

But in a declaration in conflict with UK policy, the Christian Democrats bluntly stated that Turkey could not hope to join the EU any time. "Full membership is no longer our goal."

• Additional translation by Pawel Swidlicki of Open Europe