Only just seen this thread, so sorry for jumping in late.
If the power supply on your laptop will run on 240 volts, then you need only the plug adapter to be able to physically connect it to a British wall outlet.
If the supply is designed for 120 volt input only, then you will need to run via a transformer, and the size of transformer needed will depend upon the power drawn by the computer.
Both the allowable input voltages and the required power should be marked on a label on the laptop's power supply.