West of Putney, you can follow the River Thames towpath for miles and miles. The path is cyclable all the way to Weybridge, 26 miles in all. There’s so much of interest along the way that you might as well keep your camera strapped to your wrist: the locks, the islands, the bridges. The glorious architecture spans the full range from boat-houses to Hampton Court Palace.
And of course, as a riverside path, it’s gloriously flat.
National Cycle Network route 4 will take you from central London to the riverside at Putney. Don’t follow the NCN 4 signs slavishly, though, as it takes a diversion through Richmond Park.
Once you reach Weybridge, you can put your bike on the little ferryboat that crosses the river to Shepperton. From here it’s just a mile to the railway station at the end of the branch line; there are half-hourly trains back to Waterloo, or hourly on Sundays.