Ive looked everywhere for table legs which I can screw into the wood but every table leg I see needs a minimum depth of 25mm for the wood, whereas my wood is much thinner at 18mm.
For my Imperial unit friends, 25mm = 1", and 18mm = 11/16".
Assuming you want to keep this as simple as possible, is there any reason you can't screw through the top of the table into the legs instead of screwing the legs into the tabletop? In other words, screw from the top down into the legs. You'll have screw heads showing on the top, if that bothers you.
Is there anyway to attach table legs to this thin wood? Or any other way I can make this into a table?
Often, tables are made with an apron around the perimeter of the legs that serves to 1.) stiffen the top and 2.) give the legs a better place to attach to. The image below shows a view from outside the table.
There are a few ways to accomplish this type of joint. The image below shows one such way. If you google "table top apron construction" or similar keywords, you'll find a plethora of ways to do it.
In the case of using an apron, the legs themselves are usually not attached directly to the table top. Instead, the apron is attached to the top, which is a far more robust connection than just a single screw from a leg into the top.