I found this thread when planning to cycle the Thames- and the following may be of use.....its now March 2019, so a few years on!
The idea was to see how far we could comfortably cycle in a day, as planning to cycle the Eurovelo from the source of the Rhine.
Figured 25-30 miles a good starting point, so booked an overnight stay at Egham.
We live in Marlow, and intended to catch the train to Richmond and cycle the Thames path back, but Marlow to Reading demands a few changes, and needed to book bikes in advance. There are only 2 bike spaces and they were taken-it was Feb half term and great weather so not surprising.
Instead, we cycled from home to LONDON.
Now, I may be speaking out of turn, and walkers will undoubtably disagree, but cycling the river path from Marlow to Windsor is doeable. Take the minor road behind All Saints Chuch in Marlow-the big steeple church by Bisham bridge, and the road passes the lock, and weaves through a housing estate. Pass over a large field to your right and under a bridge and you're on the river bank. There are fields to cycle across on route to Bourne End, and the railway bridge to carry your bike across after Boune End marina, swing gate styles to squeeze your bike through, and sections through sailing clubs and housing where signs ask to dismount. Otherwise, I haven't been asked not to cycle by passing walkers. It's a beautiful, scenic, quintessential English setting, and a shame to stick to the roads.
We did decide to cycle by road along side of the river from Cookham to Taplow, just because I remember there being little wriggle room along the path, and we were getting a bit fed up of sloshing about in mud at the stiles.
The river road, over Taplow bridge takes you via Bray along the Thames, Dorney Lake and new Windsor. The cycle route suggest to follow the Jubilee river, and its a pleasant cycle, but again I've never had difficulties or objections cycling the former route.
From Windsor to Egham, I searched every way to continue the river, but it seemed impossible, so we took to minor roads, bisected the Long Walk and cycled Old Windsor to the Devere Hotel (kindly, they let us use their luggage room to store our bikes overnight). We'd only cycled 20.4 miles, and realised that we could have easily added on another 10 miles today. Cycling on the flat is so much easier!
The next day, I really wanted to cycle past Runnymede Magna Carta monument, which meant the river path, rather than the busy road. It is a footpath and not a cycle route, but again, no issues cycling it. The road is close to your right, so any objections meant that we could easily zip onto the road.
Passing though Staines via the river and then to Chertsey, I knew here, at the Kingfisher inn, we would need to cycle route 4 along the road, as the river fragments. The cycle path is well marked and rather than the busy road, keeps on a designated part of the pavement.
The last section into London, surprised me, as the scenery remained wonderful, paths widened and it hardly felt like we were in the largest city. We did need to navigate though the busy streets to refind the path, but cycle route app that I'd downloaded was really useful and stopped me getting lost a few times.
Hampden Court, we could not resist pushing our bikes to the cafe in the grounds and enjoying a coffee, before cycling the last leg to Richmond train station. With difficulty, we spotted the centre train carriage to take our bikes- no reservation required, and got back to Reading, where we were collected, loaded bikes on car racks and back in time for supper. My tracker had stated a total of 46.6 miles. The second day, had been easy cycling too, and we realised we could have done the lot in one day.
But, the answer is that 80% is accessible by the river path and the other sections generally well marked out for cyclists. The paths were quiet, except in London, but later in the season may be busier.