It is still a little way off from the capacity of just over 85,000, plus an additional 2,000 places and 400 police and court cells for use in an emergency.
Ministers have pledged to increase jail capacity to 96,000 by 2014.
The prison population has increased by 3,000 in two years despite some 2,500 inmates released early every month.
The ministry says the increases are due to longer sentences, changes to the sentencing regime - such as jailing prisoners for life - and more released prisoners being recalled from their licence.
But prison reform activists said the population figure was a "measure of the mess in our prisons".
Juliet Lyon, director of the Prison Reform Trust, said the money spent on building jails should be used on crime-cutting schemes.
"It is difficult to see how Government can continue to waste billions building more prisons while ignoring the reasons why numbers have shot up," she said.
"Given the pressure on public spending, ministers must break their addiction to imprisonment and make better use of cost-effective ways to tackle the causes of crime."