I'm going to post a milder version of Sheik Paul's answer.
In the UK, refusals are tied to a person, not a passport or nationality, and embassies record your fingerprints, so they definitely have means of catching you.
There are obviously two options: entering visa-free or applying for a visa. The latter is clearly a lot safer.
Because, unlike in the US, a UK visa is not merely a permission to apply for entry, but a pre-approval of entry (hence why it's also called an entry clearance).
Secondly, by obtaining a visa, your previous issues with UK authorities will be eliminated as a factor. It only costs £87, and, to my knowledge, only needs to be obtained once - once it expires you can enter visa-free and you're still cleared of this specific issue (your previous refusal) thanks to that one visa you got.
If trying to enter visa-free now, you really should bring all pieces of documentation that you would attach to a visa application (for example, a couple of consecutive bank statements, invitation letter from your friends and family clearly stating the duration and purpose of your trip as well as their relationship with you, return ticket, and any and all other documents supporting the purpose and duration of your trip). Of course, don't present all of this upfront, but on request.
Even with this, it's likely you'll be delayed, though you'll probably be let in. Sheik Paul was unlucky and got to spend 6 hours in secondary inspection.
Whilst it's not very likely your experience would be this extreme (in part because your issues with the UK were in a much more distant past), still, the most stress- and risk-free route by far is obtaining a visa.