I found the following flight option for you on Expedia. Connection time is not too bad and the fare is reasonable. The outbound flight on KLM leaves from London City via Amsterdam. The inbound flight on Air France arrives at London Heathrow via Paris though. And you'll be spending the New Year's night in the plane. :)
Fare: US$ 412.40 incl. taxes and fees (around GBP 270.-- these days)
Outbound:
31st Dec. 2008 - KLM 1564 - LCY-AMS 4.55pm-7.15pm
31st Dec. 2008 - KLM 553 - AMS-CAI 9.00pm-2.15am (next day)
Inbound:
31st Jan. 2009 - AF 503 - CAI-CDG 7.30am-11.25am
31st Jan. 2009 - AF 1480 - CDG-LHR 1.25pm-1.45pm
Hope this helps.