This is the newest addition to Cycle Orbital (January 2025), and falls entirely within the Oysterzone - but in all other respects fulfils the criteria for inclusion admirably. 75% offroad and mainly through parkland - Royal deerpark no less - it felt churlish to exclude such a rewarding ride.
Barnes station lies within Barnes Common so you set off on a wide footpath (to avoid the South Circular Road) to traffic lights where you join NCN4. After a mile of Priory Lane cyclepath 1.3 enter Richmond Park, turning L 1.7 on a traffic free path up to the Royal Ballet School, White Lodge.
Turn R at the popular Pen Ponds cafe 2.6, and at the junction 3.6 there is the opportunity to stay with NCN4 straight on for Kingston via Teddington Lock: the spoke turns L to stay in the park a little longer and reach Kingston Bridge rather quicker. At 4.5 exit park, take 3rd R Tudor Rd for a mile of Kingston suburbs to 5.5 Kingston station. A cycleway rejoins NCN4 and skirting the town centre crosses 6.0 Kingston bridge. (on the N bank L on NCN4 will take you on a wide Thames-side ride to Hampton Court - Palace and station - and Spoke 6).
6.2 R on Church Grove then 6.5 enter Bushy Park, and on rather flatter terrain it's another two miles of the same: fine parkland and if you haven't met at least two herd of deer, you've been staring down at the path before you! At 8.1 you exit the deerpark, but there remains the delightful Cobblers Path to traverse - passing equally delightful Hampton open air (heated) swimming pool - until roads are reached 8.5. R and L on Manor Gardens, and it's a short quiet suburban ride to Hampton, where Spoke 6-7 takes over.