I am retired and married to a UK citizen. We file separate tax returns in the USA under our individual social security numbers. We own our primary and only home in the UK can we deduct the interest on the house when filing our US yearly taxes.

Also we both are over 68 and work small part time jobs, do we also have to report earned income to the US if we are not eligible for employment taxes in the UK because of the little amount we make is not taxed.

Every U.S. citizen and resident must report worldwide income on the tax return.

Thanks for the response. Could you answer the question regarding mortgage interest paid on the house. Can we take the interest off our yearly TAX reports in the US.

Yes, if it meets the requirements.
This is from IRS Publication 17, page 155:
Generally, home mortgage interest is any interest you pay on a loan secured by your home (main home or a second home). The loan may be a mortgage to buy your home, a second mortgage, a line of credit, or a home equity loan.
You can deduct home mortgage interest if all the following conditions are met.
•You file Form 1040 and itemize deductions on Schedule A (Form 1040).
•The mortgage is a secured debt on a qualified home in which you have an ownership interest. (Generally, your mortgage is a secured debt if you put your home up as collateral to protect the interest of the lender. The term "qualified home" means your main home or second home.)
Both you and the lender must intend that the loan be repaid.