This sounds like a thoroughly deplorable policy. In the first place, the authority, through the education welfare service, plays a major role in promoting school attendance, for which it is legally responsible. Targets for improving attendance ought to be a part of an agreed strategy between the LEA and schools. The idea of penalising the school for falling short of the targets is eqully unfortunate and is likely to arouse the ire of both governors and parents.
As to whether they can do this, only a reading of the authority's scheme of delegation can provide an answer. If there is provision for withholding funds, under certain conditions, then they are presumably acting within their powers. If not, your governors may have a case for referring the matter to the Secretary of State.
Please send your questions to Archimedes, The TES, Admiral House, 66-68 East Smithfield, London E1W 1BX. Archimedes regrets he cannot enter into any private correspondence