No its not right..
Well you could probably figure it out, but if caught you would be arrested for driving without a licence.
Car licences obtained after some date (think its 1979) only entitles you to ride a 50cc moped ON L PLATES without needing a CBT, if you wish to ride a 125 on L plates you have to do a CBT.
125 Eliminator is crap. Looks the part, but does 60mph down hill with a tailwind, and is generally laughed at for talking the talk but not walking the walk if you catch my drift.
If you want a workhorse 125... get a honda... if you want fast, get a whiny aprila, if you want comfort and commuting/fuel economy, get a Honda CG125.