Pudgie's mom has asked a very good question:
You definitely need to find out, first, whether there are import restrictions on parakeets in the UK. If you need some kind of health certificate for them, the last place you want to find that out is at the airport or port where you land!
You may also need to have information about the types of wood in their perches and toys, and probably you'll need the original containers for their food so you can show what it is and where it's from. (I don't know ANYTHING about UK customs laws, but a lot of countries are cautious about any kind of animal or plant-based material that is brought in, in case of parasites or disease.)
Pudgie's mom also makes an important point about making sure they will be kept warm during transport (and that means the entire transport - if their travel cage might be left outdoors in harsh temperatures for 20 minutes on some loading dock, that's not safe).
Would you be traveling with them? (If not, who is making sure they are fed and have water?) If you are with them, they will probably be okay on either type of trip, although they might get ticked off about not getting to come out of the cage.
Be sure you have a good cover for the cage, and remove ALL items that swing or could injure a bird during a sudden lurch. No sharp or pointy stuff. Make sure all cage doors and windows are secure (I use quick links), and also check to be sure your travel cage is sturdy enough that it won't come apart in some way if it gets bumped or something. And don't trust plastic fasteners to hold the cage together!
