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urgent trip to london
You can take the Eurolines buses which, I think, go from Gare du Nord.
Not sure it's the cheapest, but for your timing, by far the most convenient is to take the Eurostar train. The buses/coaches are by far the cheapest, but take at least 5-6 hours each way, and flying about the same once you add in waiting times and transfers from airports.
Cheapest is the bus.
Drive / channel tunnel.
If you drive via the tunnel, leave the M20 at junction 10 and follow the signs to "International Station" (Ashford), park there and take the high-speed train to St.Pancras, there is one every 30 minutes and, unlike Eurostar, it is unreserved and there are no pre-boarding checks, so you just get on the next one (having bought a ticket, of course).
Unless your actual destination is on the very outskirts of London, this is much quicker (and probably much the same cost) as driving the whole way.