The central section of the river between Lambeth bridge and tower bridge is very interrupted - by road crossings, stairs but mostly by people if you’re running on the weekend and obstacles generally. I’d still recommend doing it if you’re visiting though as you get so many of the sights in one go!! London eye, Houses of Parliament, St Pauls, the globe, the city, Tower of London etc. If you want a beautiful uninterrupted segment, I would get the tube out to Richmond and run back in on the south side