I have a Honda CD250U which is a bit like the CG125 but with a 250cc parallel twin. Nice bike and much more go than a 125 (I did my test on a CG and it was slooow).
If you want something very cheap then take a look at the old 2-stroke 100s. My first bike (which is currently for sale

) was a Yamaha RXS100, it was good fun to ride and fairly nippy if you keep the revs up. Likewise the old MZ 125s and 250s are very cheap but pretty rough and ready.
I'd echo the comments about avoiding anything Chinese. I have a friend in Plymouth who had a Lifan 125 whose frame snapped - I've seen it in the flesh and it's pretty worrying!
If you're considering getting a bigger bike, do it now! The test is getting much more difficult in October this year, so do it before then to save yourself lots of hassle. Bear in mind also that instructors and test centres are seeing many more bookings than usual due to people wanting to avoid the new test, so be quick.
99% of people will find a 125 infuriatingly slow after a couple of months and will want to trade up, so I wouldn't buy anything new. Get something old and knackered, do your test and then buy the bike you really want. Just be realistic about what sort of power you can handle straight away.
[img]http://i31.photobucket.com/albums/c390/chrisd87/DSC00749.jpg[/img][img]http://i31.photobucket.com/albums/c390/chrisd87/med_gallery_128_45_1416415.jpg[/img]
Sarah - 1970 Minor 1000 2-dr
Maggie - 1969 Minor 1000 4-dr