I see that link above goes to one of my (lengthy!) posts, so I'll try to simply summarise here:
1. You're not eligible to travel under the 'Visa Waiver Program', which means that . . .
2. You must apply for a visa. That means that . . .
3. You must get hold of a copy of your police record, and the original court record, and submit it to the US Embassy and . . .
4. You must attend an interview at the Embassy (in London).
5. If the 'GBH' offence was under 'Section 20' (i.e. 'without intent) then the US authorities may well decide that it doesn't qualify as 'moral turpitude' but if it was under 'Section 18' (i.e. 'with intent') then they almost certainly will. That's because 'assault with intent to kill, commit rape, commit robbery or commit serious bodily harm' is classed as 'moral turpitude', as is 'assault with a dangerous or deadly weapon', but other forms of assault aren't.
6. If your offence IS classed as moral turpitude then US law places an AUTOMATIC lifetime ban upon you entering the USA, so (in the first instance) the US Embassy MUST refuse you a visa. You can then seek a 'waiver of permanent ineligibility' but the whole process takes many, many months. (As I mentioned on the other thread, someone here has reported waiting 15 months before being refused).
7. If your offence is NOT classed as 'moral turpitude' the US Embassy has discretion as to whether to grant you a visa or not. (i.e.there's no automatic ban but that still doesn't mean that you'll get a visa). They generally make a decision within a few weeks of the applicant's interview but some cases are referred to Washington for 'additional processing', adding several months to the process. (Remember, as well, that there's quite often a long wait for an interview in the first place).
8. It would be foolish to book your travel before finding out whether you can get a visa or not, so I'd advise starting the visa application 9 months before booking (not before travelling) if you think that your offence won't be classed or 'moral turpitude' or 18 months before booking if you think that it might.
http://london.usembassy.gov/cons_new/visa/callcenter/add_processing.html