Dover handles both cross-Channel ferries and cruise sailings, so it is worth double-checking which terminal your cruise line uses before you travel — the port has more than one, and a driver briefed on the right one avoids any confusion on arrival. From London, the M20 and A2 are the usual routes, and as with any motorway run out of the capital, weekday rush hour is the time most likely to add to the journey, so an early start on embarkation day is generally the safer choice.
Cruise transfers tend to involve more luggage than a typical airport run — often a full-sized case per person rather than a single bag — so it is worth confirming your group size and luggage at booking rather than assuming a standard saloon will do. An estate, MPV or 8-seater is usually the better fit once you are travelling as a couple or family with a week or two's worth of luggage between you.
Cruise lines generally ask passengers to arrive well ahead of the sailing time for check-in and baggage drop, so building that buffer into your pickup time, rather than timing it to the departure itself, is the safest way to avoid a rushed embarkation.