Direct flights from the UK to Vietnam (Ho Chi Minh City in the south or Hanoi in the north) take 14 hours, and Vietnam is about GMT+7, so expect some jet-lag. You can also change/stop over in Moscow, Hong Kong, Bangkok, Singapore, Tokyo, Taipei or Doha, or make your way to Paris and pick up a direct flight there. There's a third international airport at Da Nang in the centre.
It may not be eco-friendly, but flying is the fastest and safest way to travel within this long narrow country. Hanoi to Ho Chi Minh City is about a two-hour flight. International driving licences and car-hire are almost non-existent within Vietnam; you can hire a car with a driver, but even then, you’ll probably finding travelling on Vietnamese roads a bit nerve-wracking, especially with kids. Buses aren’t comfortable – you may not even have an allocated seat and end up sitting a tarp on the floor at the back. Trains aren’t much better – even if there are only a few passengers, they’ll be hoarded onto one carriage (with sneaky ‘upgrades’ to the empty carriages sold on by opportunistic ticketing officers).