The Chilterns, especially the scarps from Bradenham to Tring are good for sightings of roe deer and muntjac. If you are careful you can get quite close. Also a good area for birds e.g Goldcrests.
Plus red kites are almost guaranteed, and buzzards likely too.
Or how about Thursley Common in Surrey? Off the A3 near Godalming, it is a huge expanse of open heathland, with a 2.25 miles trail that includes a lengthy boardwalk over the wetter parts. Save it for late spring/early summer when you have a chance of seeing lizards and snakes.
(If you're into reptiles there's a large public site just on the west of London where you can see adders in early May, PM me for details if this interests you.)
Depending on what part of London you're in, your local Wildlife Trust will have a round-the-year programme of group walks for anyone to attend to see birds, badgers, bats or whatever. There are groups for London, Herts & Middlesex, Essex, Kent and Surrey, check your local library for leaflets, or there should be info online.