Question: Will our rental income from our house be eligible as taxable income that we can use to add to our US retirement accounts?
In order to contribute to a US retirement account you must have "taxable compensation" which generally means wages or self-employment income. Rental income, interest, dividends, and other types of passive income do not count.
However, in your case you say you are getting a UK salary, which can be considered taxable compensation, but be aware that any amount you exclude using the foreign earned income exclusion is not taxable compensation. There is no such issue if you take a foreign tax credit on your salary instead of an exclusion, so you may wish to consider using the credit instead.
Also, you didn't ask, but some unsolicited advice: there are UK tax savings available if before becoming UK resident you contribute to both Traditional and Roth IRAs, then once in the UK you contribute to the traditional IRA and then immediately do a Roth conversion. This opportunity is discussed in a few threads on this board - here's one:
http://talk.uk-yankee.com/index.php?topic=80620.0