To get a random couple of weeks during the summer, knowing someone is really important. Sending cold letters (i.e. to people you don't know) will only really work with much smaller companies. However, if you are a taking a gap year, there are loads more options - several firms, such as Deloitte & Touche and PriceWaterHouseCoopers, offer 6 month long programmes, paying well in exess of £10,000. (These are clearly very competitive, but if you think you're in with a chance of an Oxbridge Economics place you have nothing to fear).