I have just been put on the council housing list and at the moment live in a 2 bed house in which the 2nd room is tiny. The council are saying that my two daughters, aged 16 and 1 year, can share a bedroom.
I thought once a child hit secondary school age they should have their own room?
Are they explicitly saying this, or are you assuming they're implying it, because you're in a 2 bedroom house?
I can only speak for the US, so YMMV, but legally speaking, housing supports up to two people per room. In your situation this means that they can give you a 2 bedroom place and tell you to deal with it, but they can't give you a 1 bedroom place. Given the differences in cost (not to mention availability) of 3 bedroom places vs 2 bedroom places, it's not surprising that the implication is that someone has to share a room with someone else.
That said, assuming the actual decision is yours, it's ultimately up to you. It's not uncommon at all for siblings to share a bedroom all the way until the time they move out. Where it generally becomes a taboo or sticking point is if the children are opposite genders (for countless reasons). However, you don't have that particular issue.
Your issue isn't so much about your older daughter being a teenager as it is about the age difference between your children. Both have vastly different needs and schedules, and they both need to be taken into account. Putting them in the same bedroom will likely cause issues with sleep as the teenager runs the risk of waking the little one and vice versa, at a time when sleep is extremely important for both of them.
They don't need to share a bedroom, though, at least for the time being. Your 1 year old can share your bedroom. You can also get creative with other rooms in your house and create a bedroom for someone. For example, if you have a finished basement or livable attic, you can turn it into the teenager's bedroom (many kids love the sense of privacy that having an entire floor to themselves brings). You could also section off the living room or some other room to create a bedroom for someone.
Assuming you're in the UK, a child of 16 or over should indeed be entitled to their own room: http://www.housing.org.uk/policy/welfare-reform/bedroom-tax
