There are a number of reasons why one might want to change the Definitive Map and Statement and different pieces of legislation are required depending on the reason for the change.
The Wildlife and Countryside Act 1981 is used to register unrecorded public rights of way, including registering higher levels of rights over a route that is already shown on the Definitive Map and Statement (e.g. bridleway rights on a route recorded as a footpath). It can also be used to alter details about a recorded right of way if it can be shown that they were incorrectly recorded.
The two main pieces of legislation used to divert and extinguish existing public rights of way or to create new ones are the Highways Act 1980 and the Town and Country Planning Act 1990. The relevant legislation for what you want to do will depend on your reason for wanting to effect a change.
The links on the left are to pages that explain these three pieces of legislation in more detail.