How to go?

By train. 2 1/2 hours.

Well, up to a point, Myriam...

Your choice:

- bus to Victoria coach station, then change for a bus to Dover. 4.5 hours
- tube to Victoria or Charing Cross railway stations, changing at Hammersmith, then train to Dover. I'd say you'd be pushing it to do it 2.5 hrs, but with a fair wind...
- Heathrow Express to Paddington, tube changing at Oxford Circus to Victoria, then train. Probably just about the fastest.
- the cruise company's bus, if a cruise is what's taking you to Dover
- pre-book a cab. This will not be cheap.

With bulky luggage, the steps at Victoria tube station really are tricky. I actually saw some buffoon leave bags unattended there the other day, while he tried to carry them up the steps one at a time. Do this and you're liable to bring the whole of the transport system to a halt (and find yourself very unpopular as well as, along with a couple of million other people, missing your connection).

With any luggage at all, you really don't want to try to get to Victoria Coach station from Victoria tube station, which is why the bus journey is probably the least painful.

If it was me, I'd investigate hiring a rental car. Although it's a busy road and over 100 miles, it's divided highway pretty much all the way.

Flanneruk, I though: a short question requires for a short reply!

If style matters more than being helpful.

as flanneruk's detailed answer shows - there is no easy way to do that connection. If you are indeed taking a cruise out of Dover -- just use the cruise lines transfer option. Even if it seems expensive it is likely to be the easiest and fastest way to get there.