Parkrun is a national scheme setting up timed 5km running races every Saturday at 9am at parks around the country.
Its completely free and if you want a recorded time all you have to do is signup online before hand at the link below.
Starts 9am Prompt from outside the Lido. Just turnup and run
Two laps of the inside of Brockwell park.
Register on the site & Printout a barcode and hand it in at the end if you want official timing.