How to avoid paying tax in US as well as in UK, on rental income in UK?

If you pay U.K. tax on the rental income you might be able to claim the foreign tax credit on your U.S. tax return to reduce or eliminate the double taxation. Also, there is a tax treaty between the U.S. and the U.K. that might have a provision to reduce or eliminate the double taxation. This is a very specialized area of tax law. I assume that you live in the U.S., since you said that you have a salaried job in the U.S. You should find a local tax professional who specializes in U.S.-U.K. taxation. The tax pro will be able to look at the details of your situation and tell you how you can avoid paying tax to both countries on the same income.