From your comments, may we make some assumptions?
You were born in the UK, or at least outside of the USA. One, or both of your parents was/is an American. You were registered at birth as an American at the US Embassy or you provided evidence of being an American (via parent(s) data) at the time you requested the SS card. Your US Social Security card does not have words to the effect - not valid for employment - written on the front. You did not obtain the card in order to allow someone (including non-US parents) to claim you as a dependent on a US tax form.
If all of the above are true, then (IMHO):
1) you have acknowledged to the US, via obtaining the SS Number and providing evidence, that you consider yourself a US Citizen.
2) the US has acknowledged, via issuing the SS Number without restrictions, that they consider you a US Citizen.
Now, the tricky part.
As a US Citizen, you have the obligations of an American abroad which include filing tax and information returns yearly if you meet the relevant thresholds. You are on record as a citizen. Your situation would be the same if you had not obtained a SS Number, but the chances of 'masking' your citizenship would have improved.
You may be familiar with the term FATCA. It is a US law which requires all banks, building societies, etc., worldwide, to request you to make a declaration of all your nationalities when opening a new account. That information is then passed to the US IRS via HMRC. It comes into effect 1 July of this year, although as I understand it some UK high street banks are already asking the question. You could lie (or have a lapse of memory), but if discovered the consequences could be severe.
If you wish to tackle this above board, then you have a decision to make. Do you ever wish to live in the US? If so, make amends and file as required from here forward. Would you prefer not to have US Citizenship with its attendant obligations? If so, then you need to investigate renouncing your US Citizenship. But, be aware renouncing properly requires 5 years of past US tax returns completed. You also need to investigate FBARs.
I would suggest contacting the US Embassy at this time to request a written statement that, as a US Citizen, you are exempt from reporting will be a fruitless effort and will only heighten awareness of your situation. It's unfortunate you were told this, but it does give you reasonable cause for not filing until now. Could I ask in what year were you told this? I'm guessing it was not recently.