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I've been working on this one for a while. They said it couldn't be done (the voices in my head, that is), but I've proved them wrong. So here it is - the family-friendly route from Upper Norwood / Thornton Heath to Richmond Park - in just under ten miles.
Distance is just under ten miles each way - but as the route is a bit wiggly & there's a significant hill just after Wimbledon, you'll want to allow 1h15 to 1h30 each way. Stop for a snack at Figges Marsh or the Wandle Trail. The whole thing is a 20 miler with some hills so age wise this is probably a 9+.
On the return trip, you may be better off taking the "allotment path" out of Norbury Park (bear right after the BMX track) & heading up Virginia Road. Norbury Hill has a fair bit of traffic and when you're going uphill it's not great.
There's a railway footbridge at Mitcham so no cargo bikes on this one, sorry. (You can use the level crossing at Mitcham Eastfields instead, but it means a couple of hundred metres of Grove Road & the busy roundabout at the end. - not ideal with kids. There's an alternative to go down Acacia Road past the BMX club and back up again, but it adds another half a km on to a ride that's already quite long).
This route recommends a very short dismount (sub 200 metres) to get across the railway at Wimbledon Town Centre. There's a route further south on mostly quiet roads, but that requires a second railway footbridge, you end up dismounting either way so this is easier. It's either that or go the long way around their nasty 1980s one way system. (The 80s: Great for music. Awful for town planning.)
The surface on Wimbledon Common is kind of rough in places and may be muddy at times - don't bring your shiny £2k road bike or wear your sunday best!
Quiet route from East Croydon station to Blackfriars Bridge. This uses the most direct route through Dulwich Village - quieter version is: turn right at South Circular, along shared pavement to crossing, left in to Dulwich Park, and head north until you hit Townley Road.
This is the most family-friendly route from Norwood Lakes to the Thames Path I've been able to find. If you turn right when you get to the Thames you can come back on the Waterlink Way; left and you can come back on the Wandle Trail or Quietway 5.
A quiet streets route between Grangewood Park and Norbury Park. Please take care crossing Grange Road and Green Lane. Virginia Road tends to attract a few idiotic drivers so be careful there too.
Family friendly route from South Norwood Lakes to Crystal Palace Park and back.