The Building London Blog has covered London Bridge, and where bits of it ended up, in a number of posts: https://buildinglondon.blog/2022/02/15/30-old-london-bridge-part-1/
https://buildinglondon.blog/2022/02/22/31-old-london-bridge-part-2/ and e.g. https://buildinglondon.blog/2022/05/06/38-the-alcoves-of-old-london-bridge/
And, someday Building London WILL go to Lake Havasu, but for now, recently, a visit was paid to Gilwell Park, Sewardstone, up the road from Chingford, on the edge of Epping Forest, to see an alleged 20m section of the balustrade of the 1760 London Bridge!
Gilwell Park is now famous as a Scout camp site and site of the Scouts HQ, but was for many centuries, a large estate.  And in 1824 the estate was purchased by London businessman Thomas Usborne “… described as a “Merchant of (No.20) Cumberland Street”, probably in the timber and coal trade. He acquired Gilwell House by Epping Forest in 1824. Osborne Hall became Gilwell Hall, and then Gilwell Park.” And as well as enlarging the house, a few years later, “ When Old London Bridge was replaced in 1831 he bought the parapet and re-erected it at the back of the house”.     MOLA argue this is not correct! Go to the end.
The balustrades are clearly marked on the 1896 map!
The stones must be from the 1750s/60s rebuild of the mediaeval bridge. Patricia Pierce in her “Old London bridge – The story of the longest inhabited bridge in Europe” states “There were stone balustrades on the river side of the walkways, which, it was triumphally noted, were wider than those on Westminster Bridge.” 
A number of contemporary paintings clearly show them.
Wikipedia states “Usborne bought pieces of the stone balustrades, which date to 1209.”  This is almost definitely incorrect but has been copied to many other websites. London Bridge is that old but the balustrades are not. The sign at Gilwell also wrongly implies the same.
None of the sources state what stone they balustrades are but they appear to be a shelly Portland stone, and as it was Portland that was used to reface the bridge in 1760 that makes sense that they are.
And it’s great to think these will be the same balustrades that Charles Dickens must have looked over, as his semi-alter-ego, David Copperfield states, “I was often up at six o’clock, and that my favourite lounging-place in the interval was old London Bridge, where I was wont to sit in one of the stone recesses, watching the people going by, or to look over the balustrades at the sun shining in the water, and lighting up the golden flame on the top of the Monument.” 
However! MOLA state this is NOT from London Bridge!
MOLA disagree that this long balustrade was once part of London Bridge! They state in London Bridge: 2000 years of a River Crossing
“ … it is alleged that the baroque-style, stone balustrade in the grounds of Gilwell Park .. is from London Bridge, but examination of the balustrade suggests that this is unlikely” p167 noting that
“Comparisons of the balusters with the two half balusters in each end of the Guy’s Hospital alcove revealed that the Gilwell Park examples are 65mm shorter than the Guy’s examples and the Gilwell Park examples also have a slightly different profile” They add “It should be borne in mind that this design of baluster was very popular during the late 18th and 19thC”. 
And yes if you look at the photos above AND those of the ones on https://buildinglondon.blog/2022/05/06/38-the-alcoves-of-old-london-bridge/ it is clear that they do have a different profile.
So, maybe this balustrade is not from London Bridge after all, though it is very coincidental that it appears at Gilwell shortly after London Bridge was knocked down AND that all the literature agrees that it was once part of London Bridge, though of course myths easily arrive fro coincidence! So another mystery!
Gilwell Park is open to the public, but only by arrangement as obviously being a Scout Guide campsite there are issues with random visits. This is from their website:
“Visiting Gilwell Park
Let us know you’re coming. Planning to visit to explore our heritage and the grounds for the day? Fantastic, we’d love to have you! Please drop us an email so we can check that Gilwell Park is open to visitors on your chosen date and make a note that you’re coming to see us.
Please be aware that no pets, other than assistance animals, are permitted on-site. Smoking is only permitted in designated areas, and no smoking or drinking is allowed in front of young people.
Please be mindful when visiting, as the centre is likely to have lots of groups of young people visiting. Please be aware of our young people first policy.” https://www.scoutadventures.org.uk/centre/gilwell-park
There is a public footpath that goes through Gilwell Park, but you can’t see the balustrades from there and it would not be cool to wander in.
Also important to say that Gilwell is on the edge of London’s lung, the beautiful Epping Forest so definitely incorporate a visit to Gilwell with a long walk in the Forest!
And just up the road is the newly opened Gunpowder Park.
The Scouting Adventures instructions are:
“Our closest train station is Chingford, with trains running to Walthamstow every 15 minutes. From central London, take the Victoria line to Walthamstow, and then change to the London Overground service to Chingford.
Gilwell Park is about a 30-minute walk from Chingford – it’s a busy road with only a partial footpath, so please be careful! Taxis are available from the station if you prefer.” https://www.scoutadventures.org.uk/centre/gilwell-parkReferences
Note that you do not have to walk along the road as there are footpaths that come into Gilwell. Go across the golf course and through Hawk Wood. See the maps above for details
Cycling all the way out of London, the best route is up the Lea canal path to Ponders End then cutting across the valley, or wending your way up through Epping Forest from Wanstead or through the quiet roads of Walthamstow, Highams Park and Chingford.
 Chingford Historical Society Newsletter 19, Autumn 2019