While a small number of authorities performed well, the majority were still way behind the Government's targets according to this week's figures from the Audit Commission.
Educational psychologists, meanwhile, admit that the system nearly "ground to a halt" in some parts of the country over the past two years.
Statements of special educational need are formal descriptions of a child's disabilities, and promise help on top of what schools can normally provide.
Local authorities have been hit by a rapid rise in the number of children needing statements. This week's Audit Commission figures show that in Mid-Glamorgan and St Helens the proportion was more than five per cent in the 199394 financial year; the official target is only two per cent.
Paul Vevers, assistant director at the Audit Commission, said: "There's now a clutch of authorities who show that it can be done. There was a time when some took an average of three years to produce a draft and the reaction then was that the whole process was just too difficult.
"But there are undoubtedly some big questions to ask: how is it that some councils statement no pupils at all within the six months? Some people still have one hell of a mountain to climb."
He predicted that local authorities would come under intense local scrutiny, particularly if there is no improvement next year.
In 1992 the Audit Commission and Her Majesty's Inspectorate jointly published a damning report which said that local authorities routinely delayed the production of statements. It said that some were delayed so long or couched in such vague terms that they were worthless. This was at a time when the Government had published recommendations that draft statements should be produced within six months.
The situation had barely improved in the 1993-94 financial year according to the figures published this week. They show that metropolitan councils were on average completing only 19 per cent of draft statements within six months; London boroughs fared little better with 20 per cent; English and Welsh counties completed 33 per cent.
Despite the generally poor performance, some authorities did notably well. Liverpool managed a 95 per cent rate, for example, way ahead of the nearest metropolitan rival; Gwynedd wrote 87 per cent of its draft statements within six months, Powys and Northumberland 80 per cent.
At the other end of the scale, Sunderland, Rochdale and Havering registered none at all; Harrow, Sandwell, Doncaster and Norfolk completed only around 1 per cent.
Steve Colwill, president of the Association of Educational Psychologists, said that local authorities had been struggling to cope with the weight of statements. "The system was getting slower and slower in the past two or three years. It was grinding to a halt while the number of statements was going up year after year."
Tight new 26-week time limits have been operating since September's introduction of the Code of Practice for the Identification and Assessment of Special Educational Needs and the first indications are that the speed of help has already picked up. But educational psychologists have warned that a shortage of trainees is likely to undermine their efforts.
"The idea of the Code of Practice was, in part, to cut down on the number of statements," said Mr Colwill. "We won't know if that's successful at least for a year."
Geoff Lindsay, president of the British Psychological Society said: "The assessment and record making process should be carried out within a reasonable time. Six months is reasonable. We regret very much that authorities have not the staffing or finance to enable them to carry it out."
A spokesman for Wolverhampton said that the authority had been dealing with a large number of statements and that important reports from other agencies had been delayed. Alan Sapsford, a senior education officer with Norfolk, questioned the validity of the figures suggesting that some authorities do not keep accurate information. Norfolk, he said, had also had a heavy workload. Both authorities have recently increased the number of psychologists by 10 per cent.
A spokeswoman for Liverpool said that it had been successful partly through ensuring that a quick turn-around of statements is a priority.
She said it also has the co-operation of the local health services. Both these things were identified as important in the Audit Commission's 1992 report. Gwynedd, which came second in the table, said it had introduced a system of deadlines and monitoring for its staff.