I do have experience of this but it is from 2009;
It is not a good experience I'm afraid, I found out I was pregnant in the February due in August, I had to give up my part time supply teaching assistant job in an SEN school and looked to the government for some help - I got none, I was told that as a student I could not claim for JSA or even maternity allowance, I carried on with my course but the stress of having no money and the fact that my bump was massive (an 11lb 13oz baby) I couldn't get in after the April and ended up flunking.
I got in touch with my local MP who then got in touch with the Job Centre - They then magically worked out I could recieve Mat Allowance as I had been working the year before full time - Do you work at all? If it is part time typical student work then you probably wont get any support from them but you can try for mat allowance, with this I got £140 every 2 weeks but thats because I had a good wage the previous summer.
Our situation was slightly different because although on a low wage, my DH was working full time.
My suggestion would be the following;
Make sure you fill in all the proper forms to take the time out of uni, make sure everybody actually knows that you are pregnant and are having a baby - I regularly found that my tutors didn't know and typically the male ones wouldn't ask whether I was updiffed or just chunky!
Fill in every form from the Job Cente as possible and when you do fill them in as a SAHM not a student, I know this sounds a bit naughty but they will not support a student!
Talk to your uni, I know mine offered a £250 "Congrats" grant to new parents etc and they will be able to help you talk to Student finance about defering, or have you finished?
Fight for everything you can, otherwise they will not give it over lightly! I really struggled but in the end I got my Mat Allowance the day before I actually had my DS, it was a nice lump sum but tbh we had struggled so much before he was born that it was already spent - I couldn't get a new job whilst pregnant and couldn't claim any benefits because up until a certain date in May I was still classes as a student - I'd suggest booking an appt with your local job centre and your finance dept in uni - they will know exactly what you can get.
With regard to child benefit - everyone is entitled to that, £80 a month.
Child Tax credit - Depends on your household income I think - Mine varies but is usually between £40 and £50 a week - You may get more if you DH is part time, but I don't know