I was recently offered a position to work from home for a non-profit organization. Even though, they offered to pay me about 20 pounds per hour, I was told that I would appear to be self employed and not employed by them. I have not heard of this before, and I am not experienced with these type of employment arrangements, but does this sound legal? Please help, thank you

Yes, its legal. Your employers don't make any tax deductions from your paycheck. It is your responsibility to report your earnings when you file your income tax. Keep all receipts. There are tax breaks for using part of your home as an office, etc.
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Thank you very much for the answer, that sounds encouraging.