Russia's a very big country. (It's nearly double the size of the USA). So your journey time will obviously depend upon which part of Russia you wish to visit.
You can plan your route with ViaMichelin. The estimated total journey time, from London to Moscow (excluding check-in & waiting times for Eurotunnel) is given as 32 hours 39 minutes, over a distance of 2806km (1744 miles).
That means that a commercial driver (who doesn't stop for any sightseeing) might aim to do the trip in 3 days but 4 days might be more realistic.
You could drive there by splitting your day equally between (brief) sightseeing and driving, in about a week. However, to get the best from the trip (with several stops for a few days sightseeing each time), you'd need to allow at least a fortnight.
http://www.viamichelin.com/
Chris