Not sure about the situation overseas. However, in the US, regardless of whether you receive payment in cash or you provide a receipt, if you have income as is clearly the case here, then you are liable for paying taxes on that income.

There have been a number of high-profile cases here where wealthy/well-known people would pay their nanny's in cash and try to get around employment/tax regulations. When the IRS caught up with them, they had to make amends all around and additionally pay penalties.

Again, just because you don't leave a paper trail does not mean that you aren't liable. Can you get away with not paying the tax - certainly, but if you're caught you are guaranteed that you are going to be paying much more than you owed and additionally have your tax returns scrutinized for a fair amount of time thereafter.

I have been renting a room including some food and washing since 2004 at £200 per week. All payments have been cash and I have given no recipets am I liable for tax

If you are the sole owner of the house, any rent you receive from the roommate is considered income. The only exception is if you rent the room less than 15 days a year. If you and the roommate jointly own the house, the roommate's share of the mortgage payments is not considered income.

See IRS Publication 17, www.irs.gov/publications/p17/ch09.html, where it says: "You generally must include in your gross income all amounts you receive as rent. Rental income is any payment you receive for the use or occupation of property. In addition to amounts you receive as normal rent payments, there are other amounts that may be rental income."

The rental income is reported on Schedule E. You may be able to offset some of the rental income with expenses associated with the rental and depreciation.