In the current system, you can go stay at home and get income support, which should provide you with the basics i.e. a home, food, electricity etc. If you would like more than this, you can go and get a job and hopefully earn more (have a better lifestyle) than staying at home not working.
[Note the 'should' and 'hopefully' - This system may not always work, but when it doesn't it's generally a fault with wages paid not being sufficient rather than the benefits system being broken]
This therefore means there is an incentive to go work. There is also control, to make sure the money the unemployed person is getting is mostly spent on the basics (such as housing, rather than say drugs).
The problem with suddenly giving everyone a minimum amount of money, is that due to everyone now 'at least' having that amount of money at hand, this becomes the new 'bottom' of the market. If I get a job, I earn money on top of this basic amount, which means I can afford nice things and the person unemployed still can't afford anything.
To clarify, this works similar to pricing of items in different markets. A beer in the UK is ~£3.50 (£5 in London), a beer in Vietnam is about 14 pence. Both costs are fairly relative to what they would have to pay their work force to produce the item (plus cover costs and make a profit) and what the local market can afford to pay.
If let's hypothetically say, you gave everyone in Vietnam this basic wage, the cost of beer would not remain at 14 pence. The first reason is because the work force would find their existing pay negligible compared to the basic pay (so wages would have to rise to be incentive to work on top of basic pay) which would in turn cause cost of manufacturing to rise, but also the market would realise with this extra money available - the price could be set higher and would rise accordingly.
Now back in the UK if this was to occur, you would have slight price rises due to these factors which would in affect move the poverty line up higher, which would mean the people at the bottom are still poor relatively.
What's worse is that assuming the people who are unemployed are given the choice on how that money is spent, they may in fact not spend the money sensibly (i.e. on their housing) and end up homeless instead.
The final problem with this model is that the cost of living and economic output is not evenly distributed throughout a country. £1750 a month in northern England may give you a fantastic lifestyle, where as in London you'd barely cover your rent. (What happens to the unemployed in London in a fixed give everyone a basic income situation? They have to leave London and move where they can afford, which then makes it potentially harder to find a job and splits the country into two halves, the elite / the poor).