I can't find any web references to your phone, so I can't check its specifications. However some cheap Chinese phones only work with 2G. (e.g. here's one which another AB member was considering buying recently, until we drew his attention to it being 2G-only :
http://tinyurl.com/hsa8s2q )
I strongly suspect that your phone (or, at least, the internet side of it) only works with a 2G connection. That would explain why it worked with Lycamobile (which still offers a 2G service) but not with iD Mobile (which only provides 3G and 4G). It might also explain why you found yourself hating Lycamobile (because everything was so slow) and why the only service that your phone can 'see' is a 2G one. (iD Mobile uses Three's network, not that of Orange/EE as you've suggested)