If my Neighbour agrees (consents) to the proposed works, does that end the Party Wall Process?

If after serving the valid Party Wall Notices your neighbours does agree(consents) in writing, then yes you can proceed with your planned works, You still of course have a duty that any works carried out are correctly executed and any damage caused would be a matter for common law, but your neighbour could also change their mind and therefore trigger the Act and require an Award to be drawn up.