I am a single parent who lives in a 2 bedroom council house,I have a 16yr old boy and 2 girls of 13 and 10 who have to share a bedroom is there a law about this as I applied for a 3 bed house which was opposite but they give it to someone else with very small kids

If there are no concerns of the welfare of your children then there is no problem with them sharing a room. You as a parent are doing what you can and as long as you're safe it's fine.

If these were my children, I would put the girls with me in the bigger bedroom and the son in his own room. Or I'd put the boy in his own room, the two girls in the other bedroom, and I would sleep on a futon or daybed in the living room.

I definitely wouldn't put the three children together in one bedroom. Why buy trouble?

I agree that a 16 yr old boy sharing a bedroom with 13 and 10 yr old sisters is a concern. Laws on such things are generally very localized. I assume, by your use of the term "council house", that you are in the UK. You need to review the rules of the council. I'm surprised that they would give preference to a family with young children where gender sharing is less an issue.

Without knowing the floor plan of the house, there may be many option you have to provide some other space for your son. A basement, attic or maybe some partitioning.