Thank you everyone for your advice and support. All valuable, and much appreciated, and yet I'm still at a loss of what do I do now...
To answer some of the questions...
No, DH is not keen to accept any help from others and does not admit there's a problem. I have suggested counselling many times, he gets irritable and says he's not a psycho and doesn't need counselling. When I pointed to a message on the forum, saying a woman with 4 kids left her DH for precisely the same reasons, he said that 'surely our situation isn't that bad!' He's in denial.
Still, I find information about strategies on giving up or cutting down the gaming useful. I'm hopeful it will come into play one day, and I want to be informed/prepared.
The game is Travian. He says he plays for free, and would never pay. I only have his word for it, but he's generally very tight, so this might be true.
Changing password with his permission would be impossible as he wouldn't agree to it. Changing it without him knowing is plain dangerous. I would basically have to pack and leave the house straight after this. The video that BornSicky posted is pretty illustrative of what effect this might have on the addicted person. Now imagine a grown-up tall man acting the same way as the teenager in the video, and you will get what I mean. Basically, there's every chance it would end with violence, and given that DD is still to young to stand up for herself, and I'm pregnant, it's a silly risk to take.
bibbitybobbityhat, I'm not aware of any specialist organisations that can help with computer games addiction. It's not considered a medical problem/condition. Unfortunately.
AmyStake, I have started a diary. I think it's a good idea. Thank you. Yes, he pretty much is the only one using his laptop (Not sure what you're getting at here).
I have talked to my mum about this recently, and she said that at least he's not an alcoholic. Thank you Mum! 
cobbsie , yes he does show addictive behaviours generally - he's into computer gaming since his teens, and is rather over the top with his other hobbies too. Currently he plays another computer game, in addition to Travian, as well, and has another hobby which is his excuse not to spend time with DD. He is intelligent and very bright, but lacks social skills somewhat (doesn't know how to listen or be considerate etc) - which all means that he's more prone to escapism. Then again no one is perfect and until now I was able to tolerate and accept his imperfections. I'm not made of gold either. But right now it's different, he behaves in a totally unacceptable way most of the time, and it's unbearable.
nomedoit, and others - I have already tried ultimatums, including threatening to split up. He panics madly and is all gold for a day or two, the moment of action is gone, and in a weeks time I'm still here, and he's still playing... I'm mad at myself for not following through but he begs me not to leave and makes me feel sorry for him, so I give in. Also, by 'being good' even for a short time he reminds me of why I used to enjoy being with him so much. He's a different person when there's no laptop/internet in sight.
SpringchickenGoldBrass - we are not British, my DH is here for work, so I'm not entitled to any of the luxuries that British people take for granted. If I leave, I'd have to leave the country, which would be a massive disruption and drama for DD, and also not easy for me considering I'll have a newborn on my hands in 2 months time. I most definitely wouldn't want to leave the country before the due date, as would rather give birth here. We rent the house.
"Have you spoken to your GP?" - I was going to, about a month ago, to see GP about my stress/depression (especially in the light of possible risks to the pregnancy), and DH panicked and demanded I don't mention any of our family stuff to GP. I didn't go then. Perhaps I should.
Oh well...
Thanks again for your support, it means a lot to me.