What type of armoured cable do I need to go under the garden (screwfix
links appreciated)?

I would not export the earth for this, but use 2 core SWA cable, a local
earth rod and local TT earthing. At the garage end, have a "garage" consumer
unit with an RCD and a couple of MCBs.

Does the armoured continue to the consumer unit, or is it connected to
something cheaper once inside the house?

You can swap to standard T&E once indoors. Although this is not compulsory,
it is recommended, as much for ease of installation as cost.

Size wise, I would use 10mm, both for the T&E and the SWA. This will allow
you a 32A circuit to the garage.

If you want it on the cheap, then 6mm cable is OK for a 20A circuit, but is
it worth it for the saving?

http://www.tlc-direct.co.uk/Main_Ind...SWA/index.html
http://www.tlc-direct.co.uk/Main_Ind...rth/index.html

Christian.