Fortunately, a retinue of telephone counsellors, email counsellors, face-to-face counsellors, psychiatrists, and private clinics are on hand to pick up the pieces.
Telephone counsellors typically administer the first psychological Elastoplast. Most investment banks offer employees a free telephone number that they can call 24 hours a day - including from their desk if they want to.
Employees making use of these employee assistance programmes (EAPs), as they are known, can receive counselling there and then over the phone, or are referred for face-to-face ministrations at a later date.
The providers of EAP lines, mostly independent companies, say the grindingly long hours in financial services are one of the biggest causes of stress. They are used to fielding late night calls from overwrought staff still trying to work and panicking about deadlines.
Robert Westlake, managing director of the Personal Effectiveness Centre, which runs the counselling service for Credit Suisse First Boston (CSFB), says the best immediate advice for reluctant burners of the midnight oil is simple - 'smokeless fag breaks'.
Several one or two-minute breaks are more effective at that time than the longer breaks typically taken earlier in the day, he says.
Calls about personal relationships are also common. Philip Sanders, managing director of Personal Performance Consultants UK, which provides lines for Salomon Smith Barney, Dresdner Kleinwort Wasserstein, and Bank of Canada, says: 'People can deal with all sorts of things, but when important relationships in their private life fall apart, they can bring everything down with them.'
The company says its counsellors are trained to deal with issues ranging from work/life balance to hostage counselling.
Redundancy and other career changes are also common concerns among callers in banking, as in other industries. But Sanders says that bankers are much more likely than others to phone up with worries about relationships with their peers.
This, he suspects, is because team work is so prevalent in many areas of banking. Unpleasant, demanding or incompetent colleagues can seem that much more unbearable when experienced at close quarters and under pressure.
Some employees prefer to email rather than make a phone call. Nyasha Poe, who runs the online counselling service Friendly-Ear.com, says that contact by email can seem more discreet, making it easier to get to the heart of the problem. Stressed-out employees are sometimes willing to write something that they wouldn't want to say.
Email counselling is also handy when 'phone phobia' strikes. Phone phobic employees, often in sales positions, are afraid to make the next call - usually to a client. Brokers suffering from telephone-related problems have received emails from Poe advising that they take deep breaths before picking up the telephone.
Another solution, she says, can be to laugh to cheer themselves up before calling difficult clients.
The need for telephone and online counselling in financial services is likely to increase. Psychologists suggest that job insecurity has upped the pressure. Chris Kiddy at the business psychologists Kiddy and Partners, says: 'People aren't used to the anxiety of job loss. A lot of bankers haven't experienced anything but positive conditions, high employment, and ready jobs.'
When stress and its consequences are excessive, remote counselling by email or telephone is not always enough. Clinics offering face-to-face treatment are available for those suffering from more serious problems.
The Priory Clinic, well known for treating celebrities with drug and psychological problems, opened a branch in the City of London last month, called Keats House.
Dr Iain McGilchrist at Keats House says: 'The threat of redundancy is likely to put increased pressure on workers in the City. We are anticipating that this may well lead to an increase in workplace stress and associated addictive behaviours.'
Before Keats House opened, patients travelled to the Priory's other clinics in London. McGilchrist says that over the past six months he and colleagues have seen an increase in the number of workers from the financial sector coming forward with alcohol and cocaine problems.
Most bankers suffering from addiction are worried that their employer will discover their problem. However, McGilchrist says that this concern is often misplaced. Many seemingly unsympathetic bosses have addictive histories of their own.
Dr Neil Brener, a colleague of McGilchrist's and a consultant psychiatrist, says that employers are often surprisingly willing to help out. 'Having a senior executive off sick is very damaging. Banks are willing to invest in making them well.'
Keats House and other clinics aim to allow employees to seek treatment quickly and conveniently. The Square Mile's army of counsellors agree that long hours cause stress, and then compound it by making it hard for sufferers to find the time to get help.
McGilchrist says: 'There are sad stories of people who have let things go too far and taken on unrealistic burdens that are unsustainable. The day comes when they can't carry on any longer. When everyone else leaves they remain frozen at their desks.'