For household power, the US has 110 Volts AC whereas the UK has 220 Volts AC. Most charging adapters are designed for 110 to 220 VAC, but please verify this is the case with your adapter.
If your adapter is rated 110 - 220 VAC then there will not be any issues. The plug prongs are different between US and the UK; US has flat blade type prongs and the UK has round prongs. Also, the spacing between the prongs is different. So, you will need a $1 'plug adapter' available at most Asian stores in the US (probably in the UK too).
If your AC charging adapter is rated for 110 VAC, you cannot and should not plug it into any outlet in the UK because the voltage in the UK is 220 VAC.