Tony Blair has told Birmingham Children's Hospital it must learn to live within its means, after it warned it may have to cut services to save money.

The Prime Minister was unapologetic about the state of children's health services when he was challenged in the House of Commons.

Mr Blair was speaking after four children's hospitals, including Birmingham, Alder Hey in Liverpool, London's Great Ormond Street and Sheffield Children's Hospital, warned Ministers they were facing a funding shortfall.

Paul O'Connor, chief executive of the Birmingham hospital, said it could lose more than £2 million over the next year because of a new funding system. Hospitals are to be paid a set tariff for each treatment they perform. But Mr Blair said funding for children's services had increased.

He was quizzed by Conservative leader David Cameron who asked: "The heads of four children's hospitals have warned that vital specialist children's services may be lost this year.

"They have been battling to get this message through to the Department of Health for 18 months. Why do you think this has happened?"

Mr Blair replied: "All these four hospitals have actually received a very substantial increase in funding over the past few years - extra nurses, extra consultants. But it's important that they, like everyone else within the NHS, live within their means."

Negotiations were still taking place over the level of payment hospitals would receive, he said.

Mr Blair also attacked claims that GPs were overpaid, after it emerged that some London doctors earn £250,000 a year.

He said: It's nonsense that lots of GPs are earning £250,000 a year. The actual average is under £100,000."

It was true that British GPs were now the best paid in Europe, he said adding: "I think that is good."

Staffordshire MP Paul Farrelly (Lab Newcastle-underLyme) kept up the pressure over health funding when he asked the PM to meet him for talks about University Hospital of North Staffordshire, which is losing more than 1,000 jobs.

The trust, which runs hospitals in Stoke-on-Trent, faces a £15 million deficit.

Mr Blair replied: "It is extremely important we make these types of changes in the health services, otherwise we don't take the measure necessary to provide proper balance and accountability."

Speaking afterwards, Caroline Spelman, Conservative MP for Meriden, said: "It worries me that the Government genuinely doesn't seem to know how to stop these cuts from happening.

"They've increased health spending. The increase is actually more than the entire education budget. But we've had a number of reforms all going in different directions at once, such as foundation hospitals, funding by results, and the big increase in PFI projects."

Sandwell and West Birmingham Hospitals NHS Trust is to lose 800 jobs, while hundreds more are being lost at New Cross in Wolver-hampton, Walsgrave in Coventry, Royal Shrewsbury and Telford NHS Trust in Shropshire, and Worcestershire Royal Hospital in Worcester.