Dan... i think if they are anything like mine they will take a bit more than clay to sort them out...
Tone if you are running polished rims and have let them go you are generally on a one way ticket to hurt...
however there is a way to rescue these - i did this last year but it takes a good half day and an aching arm!!
Start off by thoroughly cleaning the wheel, preferably jet washing them
You will need;
Various grades of wet and dry sandpaper from fairly coarse to fine - i think i used the following pack from halfords
http://www.halfords.com/webapp/wcs/stores/servlet/product_storeId_10001_catalogId_10151_productId_154359_categoryId_165610_langId_-1?cm_vc=IOV4PDPZ1Bucket and water
Metal polish (autosol or belgom alu or autoglym metal polish) and soft cotton cloths
cups of tea (several)
I am guessing that your wheel rim looks something like this:

start with the harshest sandpaper and once wet work the sandpaper round the rim... you will have to get into all the nooks and crannies using the folded edge of the paper
once you are happy with the finish from one grade work your way up to the next grade
you should start to get a finish something akin to:

it isn't perfect but it is better than it was
continue with the ever finer wet sandpaper until you think that your arm is about to drop off... then continue some more, then realise that you are only on the first wheel and what the fcuk have you started and will you ever finish this, then think of ways to get someone else to do it for you.
you'll realise that there is a point that you can continue no more with the sandpaper... this is the point to stop and stretch your back and have a nice cup of tea from your Golf GTi mug

move onto the polish... the more you can polish the better the result I would say... keep using and using it... you will notice the finish start to come up slighty better



hopefully you will reach a stage where you are happy with what you have achieved:


ok, so they aren't perfect but they are a hell of a lot better than they were...
once you have got to the stage where you are happy I would jetwash, dry thoroughly, got for a short spin in dry weather to expel any water and then seal using wheel sealant or hard wax
they won't last forever but if you use wheel sealant and a non-acidic wheel cleaner such as bilberry then you will be able to keep them cleaner for longer... mine stood me from last march through to november time when the salt started to be put on the roads.. then they went to sh1t again

and no... i am never doing that job again!
ps. you might see people recommending that you pop the car on axle stands and spin the wheels using the throttle.. and then hold the sand paper against the wheel in the same spot. I think this is highly dangerous and an easy way to lose/break a finger or hand so therefore do NOT recommend that you do this.