The Exchange withdrew its pricing information agreement just as the product was about to launch after telling ESI and Sharelink that it had unilaterally altered the contract.
That decision led to complaints from the two firms who argued that the LSE was exploiting its monopoly powers.
The dispute also led to the Exchange taking the highly unusual decision to issue defamation proceedings against Sharelink's chief executive, David Jones, for comments he made about the affair in a radio broadcast.
Yesterday the Exchange said that it had agreed to withdraw its libel action against Mr Jones and also said that it had decided not to go ahead with any disciplinary procedures against the company which it had earlier threatened.
Mr Jones said yesterday: "Sharelink is pleased that it has been possible to resolve the dispute between the Exchange and ESI. I regret that this has ever become an issue and am happy to join fully in the statements made by ESI. The new Internet service represents an important step forward for the development of the private investor sharedealing and information services."
ESI had asked the Office of Fair Trading to investigate the situation and had several meetings about the matter with OFT representatives. Yesterday ESI said it was writing to the OFT to withdraw its request for an investigation of the Exchange's conduct. Dr Hermann Hauser, founder of ESI, also confirmed ESI had withdrawn its allegations that the Exchange had acted in breach of its agreements with ESI.
In an about-turn from the earlier position, the Exchange's chief executive Michael Lawrence made a statement saying: "The Exchange is pleased to be involved in the development of a service which will increase the range of choice available to private investors."
The Exchange said it welcomed Dr Hauser's statement and said that it had reached agreement with ESI with a view to ensuring that ESI's Internet service could be provided on an on-going basis.
Sources said last week that the LSE had tried to encourage ESI to find another partner other than Sharelink but that this strategy had failed when ESI made it clear that it would stick with its intended partner.
There have been problems in the past between the Exchange and Mr Jones. Last year Mr Jones spent some six months as a board member, during which time it is said there were frequent clashes between him and other board members over strategy. He has since argued that the Exchange has not fully represented the views of the private investor, preferring to concentrate on the demands of the larger institutions.
Meanwhile, APCIMS, which represents private client stockbrokers, said that it had protested to the government about the charging policy issued by Crestco, the company developing the new share settlement system. The group says that every deal of under pounds 4,000 or smaller where investors keep their share certificates will cost more to settle under the Crest system than it does under Talisman, the present Stock Exchange settlement system. It adds that under the new system individual investors will lose out while institutional investors will gain. APCIMS says the cost of an investor keeping his name on a company's register under the new system of sponsored membership looks likely to cost much more than expected. It calls for the new proposed charges to be investigated by the OFT.