There are almost 20,000 listed buildings in London, from palaces to pubs and parish churches to phone kiosks. They're particularly prevalent in inner London because that's where most of the old stuff is, and somewhat sparser towards the outskirts. There are also a few larger gaps where nothing's been listed, these generally suburbs in former agricultural areas where nothing old was noteworthy and nothing newer has proved architecturally significant. Today's question is thus...
Where in London is furthest from a listed building?
Thankfully Historic England provide a scrollable map on which every listed building is pinpointed, so I started there. This is a snapshot from northeast London, where you can see lots of listed buildings in the lower left-hand corner in Hackney, Tower Hamlets and Greenwich, and rather fewer as you continue outwards. A lot of these can be found along main roads because that's where settlement and commerce began, leaving several listed voids inbetween. I hope it's not too much of a spoiler to say that London's most heritage-non-adjacent location is on this map.
To find the largest gap I tried to identify the largest circle that could be drawn on the map without enclosing a listed building. To do this I took a roll of sellotape and moved it around my laptop screen until no blue pins were visible through the gap in the middle. I found five locations altogether, the only qualifying criterion being that the centre of of the circle had to be in London. Each centre turned out to be over a mile from any listed building, mainly because I got lucky with the size of my sellotape, and then it was just a case of measuring the radius of each circle as accurately as possible.
I can therefore confirm that the place in London furthest from a listed building is here, near enough.

This is the junction of Forest Road and Hainault Road in the London borough of Redbridge. The precise location is across the hedge in the middle of a large ploughed field about 100m south of the roundabout, but it's not public land and the entire boundary is shielded by a thickety hedge so that's the best photograph I managed to get. The nearest place you might know well is Fairlop Waters Country Park which is a ten minute walk to the west, alternatively Hainault Recreation Ground which is a large expanse across the road. The only nearby residents live on a caravan park, and although the 462 bus drives past it doesn't stop, there being no local need. Instead the land hereabouts is mostly open fields and the roads are super-useful ratruns for Essex-fringe drivers who pass through in great numbers.
So why is this the place in London furthest from a listed building? One reason is that centuries ago this was all Hainault Forest where nobody lived. Another reason is that after the forest was chopped down in the 1850s it all became agricultural land so the only buildings were three farms, none of them noteworthy. Another reason is that Fairlop Plain was acquired in the 1930s not for housing but for an airport, which when WW2 broke out became RAF Fairlop instead. Another reason is that the airfield was so comprehensively erased after 1946 that nothing of wartime significance survives. A final reason, possibly key, is that all the surrounding land then became either Green Belt or the huge Hainault council estate. That meant either you couldn't build on it or nobody built anything inspiring enough to be notable, and that's how this field became the only place in London to be over 1¼ miles from a listed building. [map] [map]
And here are the listed buildings it's just over 1¼ miles from.

» The alien-looking one is the very wonderful Fullwell Cross library, designed by Frederick Gibberd in 1959 and given Grade II status in 2007. It dominates the roundabout at the top of Barkingside High Street, and if its dramatic copper-topped drum bears some resemblance to Liverpool's Roman Catholic Cathedral that's because Gibberd designed them both. Events today include Chatty Cafe, Scrabble Club and Lego Club, or simply borrowing some books beneath the inspirational ring of clerestory windows.
» The terrace of weatherboarded cottages is 195-209 Manor Road, likely built in the early 19th century and Grade II listed in 1979. I'd never noticed them before because they're set back from the road and have since been screened behind a lot of trees and shrubbery. Their old-school construction puts them at odds with most of the surrounding suburban housing, but they are very close to Grange Hill station so make an excellent commuter bolthole.
» The first church is All Saints Chigwell Row, a fine Gothic pile built to serve the growing village in the 1860s. It was only listed in 2024, but even before that Chigwell Row had so many listed houses that my sellotape circle wouldn't have been any bigger.
» The second is the Church of St Peter, Aldborough Hatch, also from the 1860s but listed much earlier in 1979. Its building material included chunks of Portland Stone from the original Westminster Bridge which had just been demolished.
The fifth and final listed building on my circle's periphery is Furze House Farmhouse in Marks Gate. It's the oldest of all the listed buildings listed here but I don't have a photo because it can't be seen. The farmhouse is tucked away behind a locked gate at the end of a long driveway, all of which are encased so completely within a sheath of woodland that you'd think some previous owner really wanted to be invisible. Everything between here and the centre of my circle is arable farmland, hence no buildings, hence no listed buildings, indeed fewer listed buildings than anywhere else in London.
In second place is a landfill site on the Rainham Marshes.
You can't get inside the landfill site so my photo is of Coldharbour Lane alongside, a remote dead end lane that curls around the huge spoilheap to terminate alongside the estuary. Absolutely nobody lives here, indeed nobody even lives within a mile, let along in anything listed. All that's been built even vaguely nearby are industrial sites and warehouses, some of them across the river in Erith, and basically whenever you ask a "Where in London is furthest from...?" question these marshes inevitably pop up.
In third place is the 18th tee of Addington Court golf course, close to Selsdon Wood and the Forestdale estate. It won't surprise you that there are no listed buildings in New Addington, and that's mainly why these fairways are nowhere near any of them whatsoever.
In fourth place are Tolworth Court Farm Fields in the Hogsmill valley, specifically Finch Hoares, a former hay meadow alongside Jubilee Road. Nothing in Tolworth is listed, especially not that ugly tower block, and it's over a mile until you find one that is.
In fifth place, I think, is High Wood in the extremely rural hinterland beyond Orpington, beyond even the outpost of Pratt's Bottom. When I tried visiting every 1km grid square in London this is pretty much the last square I went to, so you won't have been either.
I hope I used my sellotape correctly to devise this ordering, confirmed by careful manipulation of online maps. But I do think I have the definitive answer to the question Where in London is furthest from a listed building?

It's in the borough of Redbridge in a ploughed field 100m south of the roundabout at the junction of Forest Road and Hainault Road, over a mile and a quarter from any listed building. And because it's all Green Belt round here that's very unlikely to change.