LSE's tuition fee for UK and EU undergraduates in 2014 will be £9,000 a year. (Including those who have deferred their offers from 2013). This will be subject to an inflationary rise every year of your study.
For information on the bursaries and scholarships available to UK and EU students starting a programme at LSE in 2014 please see UK and EU Undergraduate Funding for 2014. However applications for LSE scholarships have now closed for 2014.
Under the current arrangements, UK/EU students will not be required to pay any tuition fees up front. Instead, the cost of tuition will be covered by a non-means tested government loan which students will only start to repay once they have left their programme and are earning over £21,000 per year.
LSE Alumnus Martin Lewis is head of the Independent Taskforce on Student Financial Information. They have compiled a number of resources to help you judge the true cost of attending university including a Student finance calculator and from 2013 a guide: Starting Undergraduate Study in 2013 [PDF]