Almost 100 patients fit to be discharged were taking up beds at Chelsea and Westminster Hospital every day on average in October, new figures show.
It comes after the average number of delayed discharges in England reached a new high last month.
The Department for Health and Social Care recently announced that an additional £500 million would be spent on speeding up the release of patients from hospital – but health think tank the King's Fund said this is not sufficient to deal with the problem.
NHS England figures show an average of 96 beds per day were occupied by people ready to be discharged from Chelsea and Westminster Hospital NHS Foundation Trust in October – though this was down from 98 the month before.
Across the country, the average number of occupied beds has risen consistently since the summer, from 11,590 per day in June to 13,305 in September and 13,613 last month, the highest monthly figure since comparable data began in December 2021.
David Maguire, senior analyst at the King's Fund, said the problem is "another chapter in an ongoing story" as the NHS continues to deal with post-coronavirus pandemic pressures and stretched budgets.
Mr Maguire said: "It’s not crept up on anyone and is a continuation of the pressures we have seen on social care over several years.
"The sector is hitting a tipping point."
He explained that social care services have been cut due to reduced funding for local authorities, meaning many patients are waiting in hospitals for adequate care packages to be installed, such as home adaptions, places in care homes or community health support.
The difficulty of recruiting and retaining staff in the adult social care sector was also raised as a key issue.
Nationally, just 40% of hospital patients were discharged when they were ready in October.
In Chelsea and Westminster Hospital, this rose to 45% – in line with September.
Miriam Deakin, director of policy and strategy at NHS Providers, the membership organisation for NHS trusts, said: "Nobody in the NHS wants people to be kept waiting but pressure on social care and community services means that hospitals struggle to discharge people who’re well enough to leave.
"To ease pressure on the NHS, the Government must act now to fix chronic staff shortages and an underfunded social care system."
In his autumn statement, Chancellor Jeremy Hunt announced an extra £2.7 billion over the next two years would be invested in adult social care services in a bid to reduce bed blocking, alongside the £500 million discharge fund.
Some £200 million of the discharge fund is allocated to local authorities to bolster the social care workforce, while £300 million will be given to integrated care boards, which have replaced clinical commissioning groups.
Care minister Helen Whately said patients are spending too long in hospital due to discharge delays, and that the funding will boost the social care workforce, free up hospital beds, and reduce pressures on the NHS.
Ms Whately added: "The discharge fund will get more people cared for in the right place at the right time."