Firstly you will have to pay a structural engineer to specify the job so nothing is going to collapse at a few hundred pounds. Dependant on what he says and your construction anything up to £5000 I would have thought.
Secondly, Depending on the building you have this may be in appropriate work to undertake. If it is listed or historic you should ask your local authority conservation officer out to inspect it for his opinion.
Sorry to be flippant, but it's absolutely impossible for anyone to give you any realistic idea of the cost of this job. It all depends on the structure of the building, what the wall is supporting, how much support work will be needed before the wall is demolished... and so on.
As has already been suggested, you need the services of a structural engineer to guide you through this project.
As already said, you need to get a qoute specific to your requirments, also do consider especially if your house is a period property, could this alteration detract from its character. Many people love, want and expect lots of little rooms in an old property, thats part of the charm of old houses. its always sad to me to see a white open space when I enter an old terrace, all the historic charm ripped away and the atmosphere gone. Take care and be simpathetic to your house