The families of the patients have won damages, but the formula used to calculate the amount of money needed to fund lifelong care is in dispute.
The fallout could leave GPs having to pay up to £250 more a year for indemnity cover. An appeal hearing to settle all three disputes takes place on 12 November at London's Court of Appeal.
Judges in the cases said payments should be determined by the Office for National Statistics' annual survey of hours and earnings (ASHE) of care workers instead of the retail price index traditionally used to measure inflation.
The Medical Defence Union (MDU), the Medical Protection Society (MPS), Towergate and Howden Medical back the appeal.
Asgar Hassanali, chief executive of Howden Medical, said the cases were part of a raft of issues that were raising policy costs. But he said the new system was fairer.
He said: 'ASHE is more realistic but it will increase fees, especially for policies with organisations that specialise in medical insurance, by between 3 and 5 per cent over the next few years.
'Premiums are generally between £3,000 and £5,000 so it is significant. But there is now a trend away from one-off lump sum payments. Sadly some patients who need 24-hour care do not live very long so periodical payments often work out less than lump sum payments.'
Legal action brought by patients left in need of round-the-clock care by medical negligence already costs the industry £1.5 million a day, according to the MDU.
Carl Lee Thompstone was born with spastic quadriplegic cerebral palsy in 1999 and Tameside and Glossop Acute Services Trust in Lancashire accepted that it was partly responsible in June.
In May, South Yorkshire Health Authority admitted that doctors assisting with the birth of John Paul Corbett were partly to blame for his brain injuries, which left him needing constant care.
In the third case, RH v United Bristol Healthcare NHS Trust, the trust was found to be partly at fault. Insurers for the defending trusts were granted the right to appeal.
MPS chief executive John Hickey said: 'Since 1998 there have been a series of cases that have had a ratcheting effect and they are now among the highest in the world.
'We believe in fair compensation for the claimant, but also a fair deal for the public. If we do move to an index based link to earnings, there will be a dramatic rise in subscription costs. If it fails, I think it will go to the House of Lords.'