London Briefing: When is a consortium not a consortium? When there's only one member left - as CVC Capital Partners could tell you. One by one, it has watched its private-equity partners quit the bidding consortium for J Sainsbury, Britain's third-largest supermarkets group.

Kohlberg Kravis Roberts (KKR), busy with its £10 billion assault on the health and beauty retailer Alliance Boots, withdrew from the Sainsbury consortium just before the Easter break.

Then, yesterday, it became clear that remaining consortium members, Blackstone and Texas Pacific, had also made an ignominious exit from the bidding quartet in the face of continued staunch opposition to the offer from the Sainsbury family.

That leaves CVC as the sole remaining member of the consortium that astonished the City back in February with an audacious offer for one of the country's biggest retail groups.

It is possible for CVC to bring in new private-equity partners, but its chances of succeeding with what would have been Europe's biggest-ever private-equity buyout now look slim. This is particularly so as the "consortium" has only a matter of days in which to formalise its offer - it has already been given a deadline of this Friday by the City's Takeover Panel to say whether it will go ahead with a formal offer or walk away.

Shares in Sainsbury tumbled yesterday as the consortium fell apart. They crashed as much as 5 per cent, taking the price well below not only the sweetened 582p terms indicated amid frantic activity over the Easter weekend, but also below last week's 562p terms, which were rejected by the Sainsbury board.

It is possible that the board, which no longer has a representative of the founding family on it, might have been swayed by an offer of 582p. But the Sainsbury family has made it quite clear that nothing less than 600p a share will do.

Unless CVC can pull some sort of rabbit out of the hat, then the assault on Sainsbury looks destined to become one of the biggest and most high-profile defeats suffered by the seemingly-unstoppable private equity industry.

Since it first launched the move back in February, CVC and the rest of the buyout industry have come under sustained assault, accused by the unions of being asset strippers and "get rich quick merchants", who care more about their own profits than the long-term health of a company or its employees.

The onslaught served to highlight the huge profits made by the industry. Indeed, were the Sainsbury deal to go through, it has been calculated that the partners of the private equity firms involved could have collectively earned almost £500 million for themselves within four years.

It is not just the Sainsbury family, sitting on around 17 per cent of the shares, that has spurned the offer. The trade unions have been vociferous in their opposition, despite promises from the bidders that they would invest £3 billion into the business over the next five years, creating 16,000 jobs in the process.

The consortium also attempted to win over the board with the promise that investors would retain an equity stake of up to 25 per cent in the business, known as "stub equity."

But none of this swayed the family, the unions or the group's pension fund trustees, who have also played a crucial role in opposing the offer. They warned that the Sainsbury pension fund deficit could spiral to as much as £3 billion if the private-equity owners proved unable or unwilling to make payments into the fund in the years ahead. So does the bid's looming failure mean the barbarians have now been stopped, if not at the gate, then at the checkout? And has the tide finally turned against the powerful private-equity players who helped push merger and acquisition activity to a record of more than £1 trillion in the first quarter of this year?

The answer, almost certainly, is no.

The private-equity industry is still awash with cash - KKR, the legendary Wall Street investment firm whose $31 billion buyout of RJR Nabisco in 1989 was immortalised in the book, Barbarians at the Gate, is pressing ahead with its move on Alliance Boots, to cite just one example.

And not every company has a key shareholding owned by investors confident - or rich - enough to turn down what would have looked a very generous price just a couple of months ago.

They may have lost this one, but the barbarians will be back for more.

Fiona Walsh writes for the Guardian newspaper in London