There are weekly free 5ks in loads of local parks - Dulwich, Peckham Rye, Brockwell, Hilly Fields. Have a look at http://www.parkrun.org.uk/ The runs are super friendly - all organised by volunteers and very much focused on being welcoming, inclusive and fun and totally FREE. You just register once, print out a barcode and come along to the event of your choice at 9am Saturday. Not so sure about regular 10ks. There is the Chase the Sun series by RunThrough. The other good place to look is the Runners World event finder.