You are Austrian. What is the citizenship of your husband? Why are you moving to the UK? Work?
In general you can move to the UK with no restrictions. Your husband may need a UK visa if he is not a EU citizen.
If you plan to make yourself resident here, you can immediately sign up with your local NHS asnd register with a local Doctor (who works for the NHS, which is the UK's public medicine organization). You would then immediately be assigned a midwife and birth planning would commence. They are usually well organized and you should be able to sort everything out quickly.
http://www.nhs.uk/chq/Pages/1087.aspx?C ... goryID=162 is details on registering with the NHS. The key thing is that you plan to stay in the UK for a while (you can not just drop in for medical care with the intent of immediately leaving), and that you have some sort of legal status here.
You should in the mean time get a European Health card as mentioned by the previous poster. All European countries are supposed to be issuing them.