cheapest way will be to do it yourself.
The problem with this job is it will need at least a carpenter, painter and a plasterer and maybe a sparky if you want a light switch in the wall. And its note a huge job for any so it will be a little painful gettnig them imo. You might be able to get a 'handy man' to do it all bar the light switch but i often find them a little over priced as they as jack of all trades master of none so you get charged a rate generally as high as each pro but they are not as quick.
Are the tiles generic or do you have more, i wouldn't put a wall over tiles so they will need to rip up the one or two tiles in the way of the wall?
As for cost i can't help sorry as i only work with very rough places so its never one job its always 6 jobs each trade is out there doing.