I’m a British citizen with a UK criminal record for aggravated assault back in 2011, hoping to enter the US for tourism. Anyone in similar situation who can advise on my entry eligibility?
The process is clear, your chances of actually being allowed travel are not. It will likely take at least 6 months for you to obtain an answer on whether you can travel, and realistically there is no way to be sure other than to go through the process.
The process is :
(Optional) Apply for an ESTA. One of the questions you will need to answer is "Have you ever been arrested or convicted for a crime that resulted in serious damage to property, or serious harm to another person or government authority?" which, based on your question, you will need to answer as "Yes"
Your ESTA will almost certainly be denied. If by some chance it is approved, then you are free to travel to the USA under the Visa Waiver Program, but the odds of this happening are almost zero.
After you ESTA is denied, you will need to apply for a B2 (tourist) visa at your local US consulate. At the present time (October 2020) this will likely not be possible as most consulates are closed due to COVID, but once they re-open you will be able to book an appointment and go through the normal visa application process which again includes a question similar to the one above which you will need to answer Yes to.
Your visa application will most likely be denied. Technically it will depend on the exact offence you were found guilty for, but "aggravated assault" will almost certainly result in a denial. Technically this conviction results in you being "ineligible" to enter the US, so the consulate staff themselves have very little discretion in this decision - it's not that they are deciding if you are allowed enter or not, it's that the law says you are not and they can not override that fact.
The consulate staff will allow you to apply for a "Waiver of Ineligibility". This is mostly a hands-off process for you, and will result in your application being forwarded to staff in the Department of State in the US. Based on factors including the crime itself, the time since the crime occurred, any subsequent crimes you've been arrested for, etc, they will make a decision as to whether they are willing to waive your ineligibility and allow a visa to be issued. This process will take at least several months, often 6 months or more.
If your "Waiver of Ineligibility" is approved, you will be given a visa - although possibly one with a shorter than normal expiry (eg, 1 year rather than 10). If it is denied, you will not be issued a visa.