I use my US purchased laptop in the UK all the time. Simply buy one of those travel plug adaptors to convert the US plug to the UK one. Just to be safe, on the odd chance that you happen to have purchased the 1 laptop in the world that doesn't operate on dual voltage, check the ac/dc adaptor and it should say something like 120v - 240v. If you see that, you are good to go.
Same thing applies to desktops as well. Although desktops usually have a switch on the back that you have to flip to convert the voltage for use in the UK.
Edited to add: As for how to get it over to the UK, laptops are small. Carry it with you on the plane (take it out of the box it came in, of course). Buy yourself a laptop carrying case and put the laptop, any cords that came in the box along with any papers, discs, booklets that came with the computer and simply put them in the laptop case and carry it on along with your purse. A cheaper option would be to just purchase a bigger backpack and carry that on board along with your purse.