I believe that you would need to apply to the Privy Council for an Order in Council to close the burial ground, assuming that you went through the full process of planning consent and registration when you opened it. This appears to apply equally to civil burial grounds and those attached to a church.
Have you considered alternative solutions, such as tree planting to lower the water table? This could be either a woodland burial approach or a more formal tree-lined layout.
Out of interest, did the churchyard close because it was full?