Upvote:8
In the vast majority of cases, a foreign drugs conviction will leave you "inadmissible" to enter the US for the rest of your life. This is true even if the sentence was "suspended" or "spent" as these terms have no equivalents in the US.
The good news is that being "inadmissible" doesn't necessarily mean you can't enter the US. The bad news is that it's a long process to possible overcome it.
As a first step, you might like to try applying for an ESTA to visit the US and answer ALL of the questions honestly. It is extremely unlikely that this will be approved, but it only costs $21 and other than the cost there's no reason not to do it. Do not under any circumstances even consider answering any of the questions incorrectly - it may seem like an easy way out, but there are data sharing agreements in place between the US and the UK, so your odds of being caught out if you lie are high.
Presuming your ESTA application is denied, you'll need to apply for a US Tourist visa. This process requires an in-person interview at a US consulate, and currently there is a 3 and 6 month wait time to get an appointment depending on which consulate you attend.
However, as was mentioned above, you are likely inadmissible to the US, which means that the consulate staff can't issue you a visa, and your application will be denied. That's not unexpected - it's just a part of the process.
Once your visa has been denied, the consulate staff MIGHT allow you to apply for a "waiver of ineligibility". This is an application that goes to the US Department of State, requesting they waive your inadmissibility and allow the consulate to issue a visa anyway. There's no way to know if the consulate staff will allow you to apply for such a waiver, nor if it will be approved - it all depends on the specifics of your crime/sentence, and whether they believe you are likely to re-offend whilst in the US. Presuming you've kept yourself clean for the past 20 years, it's possible this will be approved, but certainly far from guaranteed.
The waiver of ineligibility process will likely take 6 or more months, and there is nothing that can be done to speed that up.
So all up you're looking at close to a year (or longer), for the possibility of receiving a visa. Only you can decide if it's worth it - but the path described above is your only option if you want to go to the US.
Upvote:10
You will need to apply for a non-immigrant visa (such as a B2 tourist visa) from the US Embassy or Consulate. The consular officer will decide on your admissibility.
See Inadmissibility waiver- Advance Permission to Enter as Nonimmigrant into the United States on the US Customs and Border Protection website
Non citizens from VWP countries who are inadmissible must apply for a nonimmigrant visa at a U.S. Embassy or consulate for authorization to travel.