Between £300 and £1300 per calendar month for a room in flatshare. It depends how much other people want to live there too. It also depends on heavily on 'perceived' desirability, and there is cause to be wary here. For instance 'Chelsea' is generally perceived by non-UK citizens to be a 'desirable' place to live. But it has little to offer young people who are renting, and young Brits don't really have it on their flatshare list atall.
There are bargains to be had, but they have to be hunted for. If the owner doesn't live in the property, then the price is often non-negotiable. You don't necessarily pay less by sharing with more people, although the bills tend to be lower. However bills don't constitute a large amount of money compared to the accommodation rent. Council tax for a property is generally not included in the quoted rent. This a property tax levied by local government and is very roughly half a percent of the property price. It varies from property to property but you should put aside around 50-130 pounds a month for it.
Similarly it is worth enquiring in advance about utilities especially during winter months. In general gas central heating is cheaper than electric heatng although the gap is narrowing slowly.