A few of thoughts spring to mind...
Firstly, I think babies and children need a quiet environment in order to speak. So, I would recommend making sure the TV and radio are off for a lot of the time. Similarly, I would encourage play with old fashioned toys that encourage creativity - dolls, vehicles, Lego. Not iPad or other electronic games.
Secondly, with this little girl I would allow extra extra time for her to speak. So, for instance, if I said 'What would you like to drink - milk or water?', I would give a lot of time for an answer to come, if necessary, repeating the question in a gentle way. If she replies, 'Milk', I would wait a moment (in case more words follow), then I would say 'Milk, lovely. Lauren wants milk. Here you are Lauren. Here's your milk'. If she says nothing, I would say 'How about milk... yes? no? ... which one would you like today? ...I can see you looking at the milk, so I think that's the one you would like. Here you are!'
Thirdly, get down on the floor and get involved in her play. For instance, if she is building a tower, make idle small talk whilst she is absorbed. Things like 'Wow, this is going to be really tall. Would you like this blue brick for the top? Shall we build another tower?'
We tend to think of child development as a race. But we're all different and have our various strengths and weaknesses. So I would use her name a lot when I spoke with her, try hard to get eye contact and just give her time to feel comfortable replying and never let her know that as an adult, you are concerned about this.
Lastly, check with the health visitor. But (and I'm really really sorry to all those excellent MN health visitors), my two HVs were not that bright and would not have had anything useful to say about this situation.
Wishing you well