The lack of staff is so acute that NHS trusts in England are spending £2.6bn a year on agency and temporary staff, official figures show.
Overall attacks on prison staff also increased, the figures show.
NHS England said: "These latest figures show our frontline staff continue to deliver an excellent service while coming under sustained pressure".
Government figures show assaults on staff rose by 12% in the year up to June 2014 - from 3,065 incidents to 3,427.
"These figures show what patients and staff already know – A&E departments are constantly running at full capacity.
Royal College of Nursing general secretary Peter Carter said: "These figures show what patients and staff already know - A&E departments are constantly running at full capacity.
At the same time government figures show that spending on agency staff by foundation trusts alone has risen by £540m since 2010 – from £855m to £1.396bn in 2013-14.
"The trust's own figures show that, in many areas, staffing levels will be below what is needed for many hours of the day.
Figures show the ministry spent £230m on staff redundancies between 2011 and 2013, £90m more than it had ringfenced for the programme.
The latest employment figures show that 88.4% of more than 150,000 civil service staff are Omani citizens.
