If I was you, I would be moving into the double to share with the youngest, and move the teenager to the single
That would be the sensible solution given that the 3 YO shares with the OP and the teen effectively has the large room to herself at the moment, but I can't see the teen liking that as she would be getting an even worse deal in her eyes. Have people missed that the teen does effectively have her own room as the 3 YO sleeps in the OPs room and almost never goes into the teen's room?
The responses on this thread indicate how skewed a lot of Mumsnetters idea of 'normal' minimum basic expectation is to expect all DCs to have their own room with no compromises to budget etc. She already has a nice house in an expensive area, which is unaffordable to the majority of the population, and yet it's still not enough.
The OP hasn't said whether she owns or rents the house or if she has enough spare money, or the energy to deal with extending the property, converting the loft or moving, so all the 'just move', 'just extend' comments are just ridiculous.
It sounds like the teen won't be happy whatever the OP does, as there will always be friends with bigger houses and nicer lifestyles, etc.
Maybe the solution is to sit down with the teen and say 'this is how much money we have and this is what mortgage/bills, food, travel, holidays, days out etc costs so if we did move to a bigger house, we couldn't have the holidays, or day to day treats, or we can't move at all because that costs £xK that we just don't have'?
Or you could get a sign like this to display? 
Apologies OP for assuming/possibly spelling it out insensitively, but people should consider that what if the OP is on her own because she is a widow and is just doing her best in difficult circumstances before wading in with the 'teens must have their own room for privacy' comments, so the OP should sleep in the lounge/move/extend etc.