Short answers, pulled from the story.
The Metropolis Management Act 1855 created the Metropolitan Board of Works effective as of December 1855. The board formally came into being on the 1st of January 1856 when it assumed powers duties and liabilities of previous commissions.
Joseph Bazalgette served as Chief Engineer for the Metropolitan Board of Works while previously working with the Metropolitan Commission of Sewers. He oversaw creation of core London sewerage system including main and street sewers which solved the problem.
Finsbury Park was acquired in 1857 and Southwark Park followed acquisition in 1864 before opening in 1869. Victoria Embankment Gardens opened in 1870 while Leicester Square opened in 1874 and Wormwood Scrubs vested in the MBW in 1879.
The scandal arose from MBW purchase of old Pavilion music hall in Piccadilly Circus in 1879 when site thought necessary for Shaftesbury Avenue construction. Music hall proprietor R.E. Villiers leased the site while paying small sub rosa amount to F.W. Goddard Chief Valuer for favorable treatment.
Metropolitan Board Works abolished by Local Government Act 1888; London County Council elected the 21st of January 1889 assume new powers the 1st of April. LCC due assume financial responsibility while MBW began award large pensions retiring officers and salaries transferring staff.