London Stock Exchange (LSE) is the world's third largest stock exchange; only the New York Stock Exchange and the Tokyo Stock Exchange are bigger. In addition to its main market it operates the AIM and trading systems for overseas securities.
Although some other exchanges, such as Virt-X, list many of the same securities, the LSE has far more liquidity than other British and European exchanges which helps it maintain its dominant position.
The liquidity created by the large pool of investors using the LSE attracts more companies to list on the LSE. This not only makes it the dominant exchange in the UK and helps it maintain its leading position in Europe, but attracts listings from further afield.
Very many large overseas companies have secondary listings in London, and a fair number have primary listings in London.
London's main competitor for overseas listings is the US (the NYSE and the NASDAQ). The high and increasing cost of complying with US regulations is attracting more companies to London.
For detailed information see the LSE website.