Mike,
Black and white. Right and wrong. Honesty is always the best policy. There is no grey area; you know what you need to do.
The thing about Self Assessment, it is just that. If you don't own up to the income and subsequently sell the property and don't own up to that then nothing will happen - unless and until HMRC take an interest and then you're in trouble.
You say you "can't afford to come clean" (by which I take it that you couldn't pay the back tax on the rental income). If you are prepared to sell the property, then the line I would take in your position (this isn't advice, it's just what I would do personally) is to make full disclosure to HMRC and use the proceeds of sale to settle any income and capital gains tax. You will probably get hit with interest but your (belated) honesty may avoid penalties. Before I took such a step, I would make sure that I had full documentation of income and expenditure (eg interest payments, repairs, management charges, insurance etc) to ensure that I could show minimum taxable income.
An acquaintance of mine had a partner who, through a quirk in the system (someone else with an identical name and similar dob) hadn't paid income tax for years. I gave similar advice and HMRC were quite sympathetic when he 'came clean'. On the whole, they're happier to tap into new tax streams than frighten people into not owning up at all and staying in 'the dark economy'.
Just a personal view. No advice intended.