It really depends on the type of photography your are shooting. Most cameras will not suffer from some exposure to rain but don't rely on the camera if it gets too wet! If you are shooting anything moving, sports, news even a wedding you need to protect the camera, not just from the rain but also from your wet hands and the wind blowing the water into the camera, lens and the nightmare water in the film chamber.
If you are photographing action like sports etc, get a coat with hood or hat with a wide brim/peak to keep the rain off the viewfinder / top plate. Make sure you can get the camera into the coat out of the elements, and that it is a breathable material so minimizing condensation.
Next is keeping the glass dry, this is not simple. First always have a 1a filter, second you need to have a dry lens cloth and dry hands to achieve this. Also rain is not just water, here in Vancouver it is clean. But in London as many big cities there is all sorts to grime in the rain so some soft paper to take the excess off first works well, but be gentle. It is also good to carry a small towel.
For the rest of your kit and film / batteries etc. Make sure the bag is water proof, from the rain and the floor where you put it down. In my experience metal cases are not as good as a ]Tenba
the canvas bags work like a sponge! My last bag I pushed 2 inches it into a sink of water and pored a bucket of water over it – not a drop inside.
A good quality camera and lenses will be reasonably sealed against a rain shower, but as soon as you are in a clean dry place give the kit the time to air off and extend all the lenses to minimum focus so the barrel is fully extended. Don't force it to dry, I have hung a Nikon in a negative dryer cupboard after i was attacked with water and it still worked!
So IMHO buy mountaineering/sailing quality gear, keep your self dry so you can focus on taking great pictures with dry cameras – and two shots Taxi in London
, Run it is raining
, to show it can be done. enjoy