On the face of it, you appear to have a contract offer that you accepted and signing. I take it that you returned a copy to the company?
The offer said that you would receive X and your dismissal date would be 30th April.
What then appears to have happened is messed up in the murky detail of what may or may not have said to you and what you agreed to.
What you do now probably depends on the size/scale of your organisation.
If it's a large organisation, suggest you approach HR and try and agree a compromise. Are you willing to stay on a bit? If so frankly the details of this should have been ironed out at the time, and HR will probably see this (in a legal sense).
If its a smaller owner/manager organisation, they are perhaps just trying to change the rules to suit.
Based on what you have said, you appeared to have a binding agreement, but no-one wants to be resorting to the civil courts to prove it.