Hi hun,
I am a housing resettlement officer in London, so thought I could offer you some advice. My job involves liasing with the homeless unit, and the allocations department to help homeless people find accommodation and set up their new tenancy.
Firstly you need to approach your homeless persons unit and ask for a homelessness assessment. DO NOT simply ask for housing forms as this will only allow your name to be added to the general housing list, and is not the route which you want to take. You need to tell them that you have nowhere to live, and are currently staying with various friends and relatives. It will help your case if you can get a letter from whoever you are staying with stating that they can only let you stay for a certain period of time, due to overcrowding/financial strain etc.
Initially you will probably be placed into temporary accommodation, which could be a bedsit, hostel, hotel etc, and is unlikely to be very nice accommodation. Evebtually you should be moved on to permanent accommodation.
I am not sure where you live, and housing rules vary across the country. In some areas, you may be awarded a priority, and may have to "bid" for properties which are advertised weekly. In other areas you may still have to collect a certain number of points, before you are offered a property. It is true that your baby will not be officially recognised as a person, who requires their own bedroom, until you are approximately 5-6 months through your pregnancy. After this point you should be eligible for a 2 bedroomed property, but may still be placed into a 1 bed/bedsit until you are housed into a permanent tenancy.
If you or your partner have any vulnerabilities, such as physical or mental health problems (including depression, anxiety, panic attacks etc), learning disabilities, drug or alcohol misuse issues (past or present), offending history, have been victim of violence or harassment (past or present), or similar, then it is important that you mention this in the homeless assessment as this has to be taken into account when working out your priority need. Also you can ask to be referred to a floating support service, such as a resettlement team, which most councils have internally, as they can help you to progress your case better.
The most important thing that you can do to help your rehousing is to be proactive and keep contacting the housing department. Even if you are placed into temporary accommodation, you need to maintain regular contact with them, and keep asking when permanent accommodation may be available to you. The more they hear from you, the more known you are to them, and the greater they believe your need to be. After all, if they hear nothing from somebody for a whole year, for example, then they would immediately think of them as being desperate to be rehoused.
Hope this helps a bit hun, good luck xxx
and congrats!! 
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