Councillor Martin Tett, the leader of Buckinghamshire County Council and chair of the LGA environment, economy, housing and transport board, was speaking at the Conservative Party Conference on Sunday at a fringe event on housing organised by the Town and Country Planning Association (TCPA).
The housing delivery test, which comes into force in November, measures councils' delivery of new homes against their local housing requirement, with penalties for those authorities that fail to deliver under certain thresholds.
The test was introduced in the new National Planning Policy Framework, published in July, which also brought in new design quality requirements.
Tett said: "Councils are in absolute cleft stick here.
"We are being beaten up under the new housing delivery test to actually deliver houses and that means planning permissions going through that, many years ago, would quite frankly not have gone through, because people are desperate to get houses permitted and then actually see them built.
"The ability to turn things down and have design discussions and to refuse on design grounds is very limited today.
"If they are turned down, we see what happens when it goes to appeal and there's political pressure on inspectors to nod them through.
"There's enormous momentum in government to get boxes built and I'm worried that the design principles will be forfeited in that rush."
Tett also said that council planning departments have been "hollowed out", leading to an "imbalance of power" with developers when it comes to viability negotiations.
He said: "Because of the financial situations they're in, lots of councils have had their planning departments hollowed out. That's the situation of virtually every planning authority I speak to.
"Many of their brightest and best have been hoovered up by the private sector. Many councils are relying on relatively junior and inexperienced staff.
"They're going in to negotiate with top-rate planning experts on the developer side.
"At the moment, we have such an enormous imbalance of power and expertise between councils and developers that this is not a fair fight.
"What we need to see is local councils being able to charge the planning fees that they set. "The govt has given them 20 per cent which is great, we would like to see another 20 per cent.
Speaking elsewhere at the conference this week, housing minister Kit Malthouse said that he would consider further measures to boost local authority planning team resources if it "becomes clear" that they are constraining development.
Also speaking at the TCPA event was Robin Hoyles, group land and planning director at developer Crest Nicholson, who said developers also found a lack of planning team resources a problem.
He said: "One of the most frustrating things for us is the quality of staff in local authorities."