I don't know what goes through the heads of people who recommend abrupt weaning? Like that happens in nature? Abrupt changes of diet of any sort aren't good news.
Basically, what I do is to go from 4 bottles a day, to three, to two, to one. I have creep permanently available, ditto hay and fresh water. They get hungry, they start eating hay and creep.
You have to harden your heart - Tex, my bottle lamb, has been shouting for the past two hours about how he's about to waste away from lack of nourishment - his fat little self and the power of his voice belie that rather 
Don't water down the milk, just reduce the number of bottles, ie open out the time between them, you don't want to fill them up with water so they have no room for hard feed & hay.
All this rubbish about lambs get bloat from eating creep and milk together is just that too, rubbish. You need to make sure that the lamb has to suck (ie the teat doesn't deliver too fast), that the bottle is above their heads so their neck is stretched up, feed no more than 1/2 litre at a time, and all will be well - the oesophageal groove closes to deliver the milk to the abomasum where it belongs, and not the the rumen where the creep and hay are.
Oh well said

I don't wean any lamb that isn't eating at least 1/2lb cake a day. So their system is already used to cake, and they are used to filling up on cake when they don't get milk. As others have said, I go from 4 to 3 to 2 to 1 bottle a day. When they're on 2, it's a full bottle twice, so their full 1L a day. When I go to 1, which is at about 7 weeks, I just cut one bottle out. If they weren't eating much cake before, that's when they realise they can fill up on cake. Occasionally I get one starts to go backwards; I will give that one its second bottle back for another week and it usually is fine when I cut it out again a week later.
All lambs need to have been eating some sort of forage - hay, grass or straw - from within the first week. They need it for the rumen to develop properly.
I know a lot of people wean at 5 or 6 weeks but I have found that they do better if I wean a little slower and later. So once they're doing very well on 2 bottles a day, and are eating cake and are at least 6 weeks old, I cut out one bottle then. I give them at least a week on one bottle to be sure they are eating cake well enough for final weaning.
Your three week old lambs will start nibbling on at cake soon. How many bottle feeds are you giving them? Give them time to get hungry between milk feeds! Put down a little fresh cake once or twice a day, throw away what they haven't eaten after 8 hours. By then it's been peed on and no-one would like to eat it!
A lot of people start the lambs on lamb creep but actually I have found mine seem happy to eat regular 16% stock mix, or a grower lamb pellet. A mix is maybe better than a pellet as there are different shapes and textures to make them interested. (Yes they often only eat the peas and flakes at first, which is irritating - but at least they are eating it!)