If the Conference League winner also finishes in a Champions League/Europa League spot, they just qualify for the respective competition as normal. If they finish in the Conference League spot, they go into the Europa League and England has no Conference League place next season. However, if Conference League winner finishes outside the European places altogether, then England would have three Europa League places next season. As happened when West Ham won it.
As it stands, all of the top sixteen (plus Southampton) still have a theoretical chance of qualifying for Europe one way or another.