Assuming you are a citizen of the UK or another Visa Waiver Program country, I will point you to the CBP FAQ:
If you were previously denied a visa, or previously refused entry to the United States, or previously removed from the U.S., your ESTA application will most likely be denied.
It does not give any indication whether ESTA approval becomes more likely with time elapsed since the denial. The extent to which that is a factor in the algorithm, if at all, would be unknown to the public. Furthermore,
If a traveler is denied ESTA authorization and his or her circumstances have not changed, a new application will also be denied. A traveler who is not eligible for ESTA is not eligible for travel under the Visa Waiver Program and should apply for a nonimmigrant visa at a U.S. Embassy or Consulate. Reapplying with false information in order to qualify for a travel authorization will make the traveler permanently ineligible for travel to the United States under the Visa Waiver Program.
As such, your best bet may be to apply for a B2 Visitor Visa