For Northwich, read Hinckley.
Hinckley Athletic used to play at Middlefield Lane in the then West Midlands league. Hinckley Town played at Leicester Road, but were only a Leicestershire Senior League team. Athletic (or the Atho as they were known) sold their Middlefield Lane ground for development and a new stadium was built at Leicester Road on the same complex as Hinckley Rugby and cricket club. Eventually Hinckley Town and Athletic merged to become Hinckley United, but it was an uneasy arrangement and eventually the club folded.
Out of the ashes a new club was formed, Hinckley AFC which was run by supporters, but because of previous disagreements over who owned what, they were not allowed to play at Leicester Road, so played at Heather for a while before agreeing a ground share with Barwell FC.
Meanwhile the owners of the Leicester Road stadium formed a new club called Leicester Road. They progressed well and have changed their name to Hinckley Leicester Road, and are currently in the Northern Premier League, midlands division one, but get very poor support. Hinckley AFC are playing in the midlands league, and despite playing at Barwell get much more support than Hinckley Leicester Road.
The sensible option was, and still is for the two teams to merge, and play at the Leicester Road stadium under the Hinckley AFC banner, but that will never happen as both sides have deeply entrenched views and the owners of the Leicester Road stadium will not allow the current Hinckley AFC to play there unless they are owned and run by them. Hinckley AFC will never agree to that, so Hinckley is stuck with two teams in the pyramid system, when there should only be one.
Sorry for the long winded reply.