Hi Nic is your puppy on a lead when you take her out (if so how can she be running around) are you taking her out at the appropriate times when she is most likely to want to relieve herself eg every hour/when she circles and sniffs the ground, after sleep,food,play,excitement. Are you standing with her as she relieves herself using words like 'be clean' that she will associate with the action, then rewarding her with a treat and praise when she finishes to reinforce the wanted behaviour.(The treats should be given intermittently then not at all once the behaviour is learnt, but continue to praise)

If you are not doing these things your puppy will not be learning anything, she needs to learn what you are expecting her to do. You need to make relieving herself outside a rewarding experience that she wishes to repeat, eventually the behaviour will become learnt.

Added you are correct, it really is best to say nothing if you catch her in the act or you may make her fearful and this could encourage her to go where you can't see it/eat it/not go in your presence.
Yes, you should make house training a priority, if you do so with a 4 month old puppy it should only take a short time to train.

Just thinking about it, we also used to clap our hands to stop her in the act when she started peeing on the floor and then rushed her outside, basically the same thing as a stern 'no' but in your case if she runs off, then a clap might help.

Also dont forget if she has already peed on the floor dont say anything and aviod eye contact whilst you clean it up.

post number 11 above continued .....
Nic as your puppy is older and vaccinated so can safely be taken out , another 'reward' you can use when your puppy relieves herself is to take her for a walk immediately afterwards. This will encourage her to relieve herself more quickly to get the reward...

Thanks everyone.
Yes she is on a lead, our garden isn't closed off so don't let her off so when I said 'runs around' I didn't mean it literally, she just roams around on the lead sniffing everywhere as if finding a spot but then doesn't
I do all of the things you mentioned such as treats, saying the same thing as she is going to the toilet etc.
Maybe going for a walk straight afterwards would be a good idea, maybe the praise and a food treat isn't working for her.
Will persevere
On the bright side she doesn't go half as often as when we first got her so at least I am no longer spending my life savings on kitchen towels!!