The packing plant is the biggest in Europe, the size of 11 football pitches, and is due to ship 1.2 million items this year.
Amazon made £7.3 billion ($14.1b) in the UK last year and employs 24,000.
Shifts begin at 7.30 in the morning and finish at 6pm, with workers given just two half-hour breaks during the day.
An undercover reporter, who worked at the warehouse for five weeks, said: "I found staff asleep on their feet, exhausted from toiling for up to 55 hours a week.
"In my five weeks I saw staff struggling to meet impossible targets, in constant fear of the sack."
He said timed toilet breaks, impossible targets and exhausting, "intolerable" working conditions were frequent complaints from the staff floor.
The revelations come at a time when Amazon has promised to improve the treatment of staff following accusations of poor conditions and low pay.
Workers in Italy and Germany have gone on strike in protest at their workloads.
On Friday more than 500 employees carried out their first ever strike at Amazon's main Italian hub, in Piacenza near Milan, over pay.
One worker in Tilbury complained: "At my induction, someone was asking why the staff turnover was so high. It's because they're killing people. My friends think I'm dead. I'm exhausted."
Another wrote on a white board for staff comments: "Why are we not allowed to sit when it is quiet and not busy? We are human beings, not slaves and animals."
The Essex plant has no natural light. Instead, fluorescent bulbs are used, preventing staff knowing whether it is day or night outside.
One colleague collapsed as they worked and was taken to hospital by ambulance. Another was seen by paramedics after suffering a panic attack when she learned compulsory overtime meant she would have to work up to 55 hours a week over Christmas.
One said: "Everybody suffers here. I pulled my hamstring but I just had to carry on. My friend spent two days off after she damaged her knee ligaments."
Some staff pay £4 ($7.76) from their £8.20 ($15.90) an hour wages to catch a bus put on by the company from London to the warehouse.
Responding to the investigation the company said: "Amazon provides a safe and positive workplace with competitive pay and benefits.
"We are proud to have created thousands of roles in our UK fulfilment centres in recent years. As with most companies, we expect a certain level of performance.
"Targets are based on previous performance achieved by our workers. Associates are evaluated over a long period of time."
The firm has also defended itself after it was revealed that ambulances were sent to its main Scottish warehouse 43 times last year.
Emergencies included 15 of the most serious Category A classification, with 23 workers taken to nearby hospitals.
Call-outs to the depot in Dunfermline involved two staff being treated for falls, a call about "traumatic injuries" and two for "industrial accidents".
A previous investigation at Amazon's sorting depot in Dunfermline found workers were threatened with the sack if they took four days off sick - even if they had a doctor's note.
GMB Scotland Organiser Helen Meldrum said: "These are shocking statistics but given the long-standing history of concern over the working conditions in Amazon, I can't say that I am surprised.
"This lends weight to our arguments that Amazon must open up to trade union recognition.
"Ultimately this is a giant multinational which has received significant public money yet continues to go about its business in an unacceptably opaque manner."
An Amazon spokesman said: "Independent safety experts certify our compliance with all relevant laws."
Last week Amazon launched in the Australian market, and has been tipped to establish a warehouse in New Zealand, according to principal of The Buchan Group's New Zealand operations David Thornton.
