Hi Amanda. I have often taken sessions in Hyde Park and while there found that the members of Serpentyne Runners seem to know all the routes in London.Try them.
Also if you run at a steady pace,why not use a gaget that counts the number of strides you take as you run.Providing you have measured your stride leangth at the pace you do a run at,it will give you a good idea as to just how far you have run.
They are quite cheap,and I have found quite accurate (usualy within 50-80metres over about 10miles)Providing you can keep a steady stride leangth.
All the best,Ron.