I think you've been looking at the Stansted Airport Express which runs to Liverpool St station and stops at Tottenham Hale.
You could use the Heathrow Express to Paddington then use the underground eastbound Circle or Hammersmith & City line from Paddington to Liverpool Street.
Alternatively take the Piccadilly undergound line from Heathrow to Holborn and change to the eastbound Central line to Liverpool Street

Or avoid stairs by changing from the Piccadilly Line at Hammersmith to the eastbound District Line, and then at any station between Gloucester Road and Mansion House to the Circle Line to Liverpool St (at Hammersmith, just walk from one side of the platform to the other; for the second change, just wait on the same platform). However, this will take a bit longer.

I'm assuming there is a reason for taking the rail/sail option, but the obvious thing would be simply to change planes at Heathrow.

Do NOT, under any circumstances, get any train from Heathrow to Paddington then change to the Circle or Hammersmith & City for Liverpool St. Especially with luggage

There may, in Calcutta or Cairo, be a more unpleasant and physically dangerous metro connection. But I've never managed to find it. Even in New York, no part of the subway system invites real injury the way the stairs down to the Paddington H&C platform does for anyone with luggage.

It's merely a matter of time before someone's badly injured or worse.

It might be quicker to get a train to Paddington, then a cab to Lpool St, than to get tubes all the way. And the train/tube option really is tolerable without luggage. But with bags: it's the worst urban transport decision in the known world.

Can I congratulate the OP for being the first person from outside the UK this decade to ask about reaching Liverpool Street Station rather than Liverpool Station.

A question for OP - why aren't you flying from Heathrow, preferably as an addition to your existing ticket so you can have your luggage checked all the way through to Amsterdam, avoid UK immigration (have you seen the queues recently) and have a connection time that means you are in some Amsterdam cafe before you have even reached Liverpool Street.

Hi to all. Thanks for prodding me with all these good questions. I will be travelling in Europe for two months before I meet my boyfriend on August 30th at Heathrow. The idea of the rail and sail sounded very romantic and that is why we are tinkering with it still. Have not yet bought the tickets for this journey though.
So, given all the good advice you have provided, we might skip the rail and sail all together.... and figure out a cheap flight from Heathrow to Amsterdam....
Thanks to all.
Cheers
Ilona

ilona_szemzo:

If you do decide to take the rail & sail to Holland on the Stella Line Ferry from Harwich please come back and share details of your trip.

Sandy

You may want to read my trip report - we did this in Sept 2010:

http://www.fodors.com/community/europe/london-to-amsterdam-via-overnight-ferry-a-weekend-adventure.cfm

Hi Jamikins,
You have just convinced me I was on the right track. We will definitely take the train/ferry to Amsterdam.

Thanks so much,
Cheers,
Ilona

I am now ready to book the train/sail package.

Wondering whether it would be better to try to reach the train station via another "greater Anglia station", instead of Liverpool St.

Which station would be closest to Heathrow, and how would we get to it ?

Thanks, Cheers, Ilona

Ilona, if you look at the map, you will see that Heathrow is in the far west of London, and Liverpool St, which is the terminus for trains from the east of London (including Harwich) is east of the centre. There is no other station for that line that would be more convenient for you.