As a general guide:
Just about all modern laptop power supplies/chargers are switched-mode units which will automatically accept a wide range of inputs (often 90 to 250 volts) without further ado. All you need is (a) a plug adapter to connect to a U.K. outlet; (b) a replacement power cord to go from the charger to the wall outlet; or (c) cut the U.S. plug off and fit a U.K. plug instead.
Some older laptops sold in the U.S. have fixed-voltage supplies designed for only 120V. For these you will need to either replace the unit with the appropriate one, or run it through a step-down transformer to convert 240V to 120V.
Desktop/tower PCs tend to have dual-voltage power supplies, but there is a small selector switch on the rear which you need to set to the correct position. Switch to 220/240V, plug in a U.K. cord, and you're set to go.
Other peripherals vary. Many newer desktop monitors are like modern laptops and will work on 120 or 240V with no selection necessary, but some are still for one voltage range only or have a voltage-selector switch on the rear. The "wall wart" power supplies which come with some printers, modems, routers, and so on are often designed for just 120V, so you would need a replacement unit or run through a 240-to-120V step-down transformer.
In all cases though, you should check the label on each device in question to see what input voltages it will accept.