You will pay council tax in the UK if you live in the property, and you will not owe property taxes on the US as these are only owed on a US property.
If you live in it you could claim tax relief on interest paid. If its an investment property that you rent out you would declare any profits from renting it, not forgetting to depreciate fixtures and fittings as prescribed by the IRS, and pay any capital gains tax due upon selling. Its not that complicated, but takes a bit of working out when the two tax years are different!