It is slightly more complicated than that. You will need to apply for an ITIN; you will then have to decide if you want to make the net election. Next you will need to file both US Federal and State tax returns; including figuring out the depreciation expense.
In the UK you will need to register for self-assessment and file UK returns using the accrual method of accounting; do bear in mind that UK government policy restricts your ability to deduct mortgage interest; which is not a problem in the States.
Separately, presumably you have some life insurance to cover the cost of US estate tax if you die while owning the property. As you are not a US citizen, the estate tax exemption is only US$60,000.