US law places an automatic ban on entry by anyone who has ever been convicted of an offence involving 'moral turpitude'. (Anyone with such a conviction has to apply for a 'waiver of permanent ineligibility, which can take many months - or even over a year - to process). However most types of assault don't constitute 'moral turpitude', so you won't have to face the really long waits that such offenders have to endure.
Even so, the rules on the US Embassy website make it clear that you must apply for a visa. (You're ineligible to travel under the Visa Waiver Program, i.e. with an 'ESTA'). Each case is assessed individually but (based upon what other people have reported here) you stand a good chance of getting a visa (unless, possibly, your conviction is very recent).
You should apply for a Police Certificate a.s.a.p:
http://www.acro.police.uk/police_certificates.aspx
You also need to schedule your interview at the US Embassy in London:
http://london.usembassy.gov/visa_contact_information.html
There are sometimes long waits for an interview but, at the moment, there is hardly any waiting time at all:
http://travel.state.gov/visa/temp/wait/wait_4788.html?post=London&x=49&y=20
Then, as that page indicates, you'll probably face a wait of perhaps around three months to hear the result of your visa application.
See also here:
http://london.usembassy.gov/b2.html
(You'll need to complete the DS-160 form)
Chris