The house that Caroline Baldwin and Brian Taylor bought has been described — and by its former owner, to boot — as “the most expensive slum in Britain.” And while £1.8 million, or $2.5 million, isn’t especially expensive by London standards, it is certainly a lot to pay for a Georgian townhouse so decrepit that the first thing the couple did was put up scaffolding to stop it falling down around them. “It was in such a bad state that we were advised we couldn’t even go in to some of the rooms in case the ceilings fell,” said Mrs. Baldwin. Now, after a top-to-bottom renovation, this former slum is a light-filled family house. And, although the restoration project cost $1.27 million, the work, plus strong market conditions over the past four years, means the house is now valued at an estimated $5.7 million. Their house, in the affluent northwest London neighborhood of Islington, had been owned for decades by Fran and Jay Landesman, an elderly and rather eccentric couple whose lifestyle has been chronicled in British newspapers by their journalist son, Cosmo. He gave their home the “most expensive slum” moniker in a newspaper article in 2010, recounting how his aging hippie parents refused to throw anything away and regarded cleaning as a “bourgeois hang-up.” After Fran and Jay died, Mr. Landesman put the house up for sale, and in 2012 the Baldwin-Taylors agreed to buy it. The couple — he’s 43 and she’s 36 — had been living in Ghana, working for a shipping and logistics company. But they wanted to return to Britain full time so that their daughter Maya, now 7, could be educated in England. The neglected house’s structural instability was one challenge the family faced. The other was that, because the house was an example of classic Georgian architecture, any work they carried out had to be approved by the local council. Initially, the couple had hoped to enlarge the kitchen but were refused building permits. Instead they added a garden room at the end of their backyard and expanded the existing basement — moves that increased the property’s square footage from 2,850 square feet to around 3,000 square feet. Along with shoring up precarious ceilings, waterproofing the basement, and restoring load-bearing walls that the Landesmans had knocked down, the homeowners’ main challenge was to conserve the house’s original features with the help of Gerard Rainey, senior architect at the firm Architecture for London. “We wanted to retain as much of the Georgian features as we could,” said Mrs. Baldwin. “The house also felt very dark, and very convoluted, and we wanted to make it as bright, and as classy, as possible.” They reclaimed original wide pine floorboards from elsewhere in the house to restore the living room floor. They hunted down a grate for the fireplace that was also of the correct period to fit the house and replaced postwar windows with modern re-creations of original Georgian sash windows. Their kitchen is an exercise in simplicity: wood cabinets painted gray; chunky, white Corian countertops and a white marble-tiled backsplash. While the palette in most of the rest of the house is pale and neutral, Mrs. Baldwin has let her love of color loose in the living room, with sofas in rich navy blue, teal and purple. Double doors open onto a study, with walls painted a deep charcoal that sets off a modern, scarlet chandelier. The couple’s master bedroom suite, one of the home’s four bedrooms, is at the top of the five-story property. The build started in July 2014, and the family moved in last April. Work continued until August on the basement, which now has a living room, bedroom and bathroom. The adjacent “coal hole” is now a kitchen. Outside, they added a decked terrace area with built-in barbecue and steps that lead down to a paved patio framed by curved, raised flower beds. Mr. Rainey worked around a London plane tree, designing a garden room with a curved roof echoing the flower beds. This room could be a study or a sitting room, but is currently being used as a guest bedroom suite. The family is now settling into their new home. “It is fantastic,” said Mrs. Baldwin. “I used to walk through this street as a teenager and think how I would love to live here one day, so in many ways it is a culmination of a very old dream for me.” This article originally appeared on The Wall Street Journal.