Become a supporter
Nice little link from Norwood Country Park to East Croydon. (Apart from a couple of hundred metres of the not-at-all-nice Lower Addiscombe Road, but that bit can be walked).
The quiet route from South Norwood Lakes to South Norwood Country Park.
Goat House Bridge is pretty nasty. You may want to dismount and walk this bit.
Croydon council decriminalised cycling in parks and on railway paths some years ago but never got around to taking some of the old signage down - cycling past Love Lane Green etc. is fine and lots of people do.
From the Country Park there are lovely routes north (Waterlink Way via Ancaster Road - to Beckenham, Lower Sydenham, Catford, Lewisham, Deptford, Greenwich), south (NCN 21 towards Shirley / Ashburton) and south-west (quietway route through Addiscombe to East Croydon).
An even better version of the already brilliant Waterlink Way (NCN 21) from South Norwood Country Park to Greenwich Riverside.
Mostly follows the official route, but uses Maberley Fields and Churchfield Rec instead of Beck Lane which is a bit of a rat run.
If you're a stickler for the letter of the law - you are supposed turn left along Beckenham Road and follow the signposted route via Kent House Station. My view is that the official route at this point was dreamt up by some cycle-hating Tory years ago - there is a perfectly good path running north from Thayers Farm Road - signposted "no cycling", but it won't cause any problems if you are considerate. Much more direct, less fiddly and, frankly, despite what the law says it's actually _more_ considerate to pedestrians: the official route takes you through the middle of a sometimes busy commuter station.
Be careful crossing Southend Lane and crossing over the railway bridge at Ladywell. You don't have to deal with the nightmare that is Catford's road system: turn right just before you hit the south circular, follow the cycle path down the slope to the station and you go under all the roads in an underpass.
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 & takes a bit over an hour. Stop for a snack at Figges Marsh or the Wandle Trail.
On the return trip, you may be better off taking the allotment path out of Norbury Park & 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 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 - don't bring your shiny £2k road bike with its feather light tyres.
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.