Other than the hassle of filing that tax record (possibly having to retain an accountant for this), it could be possible that that you do not have enough taxable/reportable revenue to declare and therefore no negative consequences if you were to file tax again. But at least your administrative situation would be settled and you would have peace of mind.
So I would talk with a qualified CPA to explore your options.
Plus there exists an amnesty program.
There is also a tax treaty between the US and the UK, meaning that the issue of double taxation is addressed. Haven't parsed all the details but understand that your pension can only be taxable in your country of residence.
From the aforementioned source:
A willfulness penalty, which may be imposed on any person who
willfully fails to file the FBAR, with the ceiling on the penalty
being the greater of $100,000 or 50% of the balance in the account at
the time of the violation. The U.S. Treasury Department reserves the
right to seize up to 50% of assets in overseas bank accounts or
$100,000 per account, whichever is the higher.
The question is, can this be enforced smoothly and easily. That will depend on the level of cooperation between the concerned countries. And the IRS first has to know a) that you still exist and b) where they can find you.
The passport revocation law, which came into effect in late 2015,
allows the U.S. State Department to revoke the passport of any U.S.
citizen who owes more than $50,000 to the IRS. It’s quite easy to end
up with this tax debt through accrued interest and penalties while
living overseas as an expat.
In theory you can lose your passport too (for plenty of reasons actually: failure to pay alimony/child support, felony etc), but you are still a citizen and not relieved of your obligations. At this point you have all the downsides of US citizenship without the advantages and you might as well consider renouncing US citizenship... possibly having to pay exit tax.
Quite simply, is my best option to just say I am a UK citizen and not
mention the US nationality?
The bank will look at your papers and say: "Sir you were born in America so you are an American citizen unless you can prove otherwise". And then, it's either "goodbye Sir thanks for visiting us" or: "your SSN please for our records, that we have to share with American authorities".
So, to carry on with your investments plans it might be sensible to sort out your tax affairs and write it off as a cost of doing business.