I looked into this a few weeks back, also as a CIC. In all honesty, there was very little that was available. I think my preference now would be to set up a basic one page website (for free) with a PayPal link (donate button etc) and use that.
Not ideal, but certainly better than nothing.
Hope that helps
This site does it for CICs subject to the activity itself being judged charitable, here's a list of CICs using it: http://localgiving.com/search?name=cic
Hope it is useful
It looks like John has found something that has potential providing they deem it to be charitable. My only problem with that would be that it is a £78 fee to set that up. Potentially, if you were organising lots of events each year then that would be very acceptable, but if it is only a one off or you expect small sponsorship then that seems quite a heavy price to pay.
Personally, I try and keep my costs down wherever possible, especially if you have the means to do similar for free (or much reduced).
Whilst that approach doesn't work with everything, if it was me, that would be the way I would look at doing it.
I assume that you will be advertising the link to the 'giving page' with whichever way you are promoting it, so why shouldn't you advertise your own link?
Yes, there may be a little more 'kudos' using an 'official' page, but most people trust PayPal as a recognised payment centre.
Having said all of that, that is just my opinion, I hope that some of it makes sense :)
You can get Gift Aid on Localgiving, so if your planning on raising more than £300 it makes sense. You also have to take into account the cost of getting HMRC approval if you do go alone and also want GiftAid
Good luck however you progress