If you get the train from Harlow to Liverpool St then you get the Circle and District lines to Victoria (if for some reason you don't like cycling), on both of which bicycles are allowed.
As previously mentioned, you could also go to Farringdon and get the First Capital Connect service to Brighton.
Epping to Central London is quite a pleasant ride, about 20 miles. It is also downhill, which is nice.
Epping to Harlow (where you can get a mainline train into London) is about 3 miles. This will be much quicker than getting the tube, since it stops so often. In fact it is possible to cycle from central London to Epping faster than the tube.
If you get the train from Harlow to Liverpool St then you get the Circle and District lines to Victoria (if for some reason you don't like cycling), on both of which bicycles are allowed.
As previously mentioned, you could also go to Farringdon and get the First Capital Connect service to Brighton.