The IRS imposes tax on everyone who earns money in the US, regardless of whether or not they are a US citizen, so you will need to file a tax return with the IRS at the end of the year. You will be filing as a non-resident alien so you will use Form 1040NR.
However, the US does have a tax treaty with the UK so you may also claim a credit for any tax you paid to the UK on this same income.
The tax treaty prevents double taxation of the same income. Whether or not you will receive any refund will ultimately depend on how much tax you paid in the UK on this same income. Since your income was from a US source, that will typically take precedence over your UK tax. So while you may not get a US refund, you should likely not owe tax in the UK.
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