"This is very confusing. If a US-born citizen has lived in the UK for most of his/her life, and is also a UK citizen with an NI number, bank account, etc... does the US still have jurisdiction over that person's income tax?"
A dual citizen has rights and obligations from both citizenships. The US deems US citizens to be "tax-resident" in the US (in the District of Columbia, I believe) regardless of where they actually live.
HMRC has primary taxing rights on UK-source income, regardless of whether the taxpayer is a UKC, a USC, or both.; the US has primary taxing rights on US-source income.
Under a recent-ish US-UK agreement, and now implemented in UK law, UK banks and financial service providers must identify and report to HMRC all accounts held by USCs; HMRC forwards the information to the IRS. Because of this law, USCs with US birthplaces are likely to receive letters from their UK banks, asking them to provide SSN and sign a US form W-9 to confirm that they are a US citizen.
You can choose to sign the form and give them your SSN, or you may prefer to renounce your US citizenship. Renouncing is easy but costs $2350. Email a US consulate, ask for an appointment, they'll send you instructions. You don't have to file any tax returns in order to renounce. It's a completely separate.
That's all. It's your decision what you do about filing US tax returns and paying US tax on top of paying UK tax on your UK-source income. The UK does not enforce or collect US taxation of UK-source income received by UK residents, and the US has little power to do so.
"I've just been informed by a tax professional that 5 years of compliance is necessary before renunciation is possible."
That's not correct. You lose your citizenship the day you swear the Oath, regardless of whether you've been filing US tax returns. The loss is confirmed when you eventually receive the Certificate of Loss of Citizenship; you can show the CLN to your bank to prove you're not a USC.
What you choose to do about your US tax obligation is a separate matter. If you have US income/assets, or you frequently need/want to travel to or over the US, you may want to jump through the hoops and enter the system and backfile the five years and file final forms. Everyone's circumstances are different. Everyone must consider the options and decide what they need to do. If you do decide to file, you could have a go at D-I-Y before paying for help.