What size Armoured Cable is needed for a 240v gate motor?

At that length and VD your probably better off looking at 6mm 3 core, 2 core if you want to stake it, depending on your supply But certainly not that classic 2.5mm which a lot of “Electricians” say Regards Adrian

I would advise that you contact a professional local electrician, as there are several unknowns in your question to give an accurate answer.

Need to know the power of the motors. However 2.5mm will supply about 5000w so you should be safe with that. Bear in mind thought that if you want the work signed off then you'll need to engage with an electrician before hand just to get their advice on laying the cable. Just reiterate. You need to work with an electrician to ensure when you bury the cable your doing within regs and you can get a certificate for the work on agreement with the electrician. You also need to ensure your laying the correct cable. No good asking on here for a definative answer if someone is telling you 6mm and another is saying 2.5.

You be better off installing an under ground cable ducting so the size of the cable could be determined at a later date - do not use less than 50mm internal dia, install a draw string / rope, run in a straight route and have easy bends where it comes out the ground, block up open ends with polythene to avoid debris getting into ducts