When we got our CKCS nearly 7 years ago our house layout was a little different and we had a dog flap in the kitchen, so as she spent most of her time in the kitchen to begin with we posted her out of the dog flap at regular intervals and as she only ever had that one exit got house trained really quickly and when we let her run around the rest of the house she used to use the dog flap if she needed a wee. However we have had an extension done and we do not have any exits outside near our kitchen.  So to housetrain our new JRT puppy (she is now 10 weeks and we have had her for four weeks as she was a rescue) we have put a newspaper on the floor in a corner of the kitchen which she will use 50% of the time if she is running about in the kitchen. The rest of the time she just wees on the floor of the kitchen.  She is crate trained, but the floor of the crate has a grid on it, so we put newspaper on the bottom and a blanket on top, so she wees in the crate on the newspaper. If we are playing with her in the kitchen we put her on the paper as soon as she starts to sniff about and say 'go for a wee'  but quite often she will run off and wee elsewhere in the kitchen.  We try and put her on the paper at regular intervals and praise her and give her a treat if she goes, but I am trying to only let her run about in the kitchen when I am in there supervising her so I can reinforce the paper, but I can do this all the time so she spends quite a lot of time in the crate which I really dont like.  She is only tiny and has a really tiny bladder (she only weighs 1800g) so I cant expect her to hold it for very long (she has no bladder infection either). I clean the rest of the floor with bio-washing powder in water and leave the wee newspaper corner alone apart from changing the paper.  I end up keeping her in the crate for longer than I like because otherwise I end up with loads of puddles everywhere in the kitchen.  I have tried taking her outside after every meal (she has four) and repeating my go for a wee command and she does go outside after a bit of running about.  Short of abandoning getting her to wee on the paper and concentrating on taking her outside every 20minutes throughout the day (which is totally impractical) I would really like her to be able to run around the lounge/dining room and conservatory which lead off the kitchen, but she just wees everywhere.  How can I let her have a bit more freedom, but get this housetraining a bit more established?

When housetraining puppies I tend to only use newspaper at night and then cover most of the floor with it. During the day the puppy is allowed to go around downstairs freely but I am always watching it and although this can become a pain as all you seem to do is follow the pup around and go outside with it every time it starts to sniff or look like it may be about to wee it pays off and the message seems to get through quicker than if you are less attentive. Although going outside every 20 mins or so may seem excessive it will work although you must stay outside with the pup and praise like mad when it goes. People with new pups have to realise that toilet training wont happen overnight and they have to work at it even though it seems like a chore at the time.

Are you feeding wet or dry food?
We found this was a big problem, dry food meant our pup drinking twice the amount of water resulting in huge amounts of wee everywhere.

It sounds to me as if you're trying to teach her two different things - one that it's OK to go in the house, so long as it's on the paper, and two, that she should go outside........  Try to think about *where* you want her to go when she's grown up, and concentrate on that, or you'll have to unteach a behaviour that you've already taught, and that's going to be much more hard work......
IMHO newspaper should only be used to minimise cleaning up, a pup should NEVER be 'trained' to use it.  This avoids the pup growing up to believe any newspaper is for weeing on - such as the Sunday papers on the doormat before you've read them ;)
To teach a puppy to go outside, they should go out after every nap, every play session, every meal, after anything exciting has happened, and every half an hour in between when they are awake.........  Stay outside with the pup (many small pups feel very vulnerable outside and their desire to be inside where it's safe will over ride any ability to relax and wee........) and praise and reward the pup outside, while they are in the process of  doing the action, not afterwards.

Smaller dogs do tend to take  longer to 'house train', but be consitent, and ensure you clean any accidents up out of sight of the pup (so they don't pick up on your annoyed body language, which will be there, no matter how hard you try and disguise it) and after doing the bio washing powder, spray it over with white spirit or white vinegar, as this helps to break up the fatty acids that hold the smell that brings the dog back to the same place.

HTH