"If the parent had not used the previous year's £3k allowance, this can be carried forward to the current year. So each parent can gave £6k in one go every two years. "
But not in the fist year of the 7 before they die. Since they don't know when they are going to die it's better to use the £3000 in each ear rather than £6000 ever two years.
But if the parents' income is higher than their outgoings, they would do better to give the money as a 'regular gift out of income'. Then it would not use up any of their £3000 annual IHT exeption which they could use in addition. There is no limit on the size of gifts out of income (except the availablility of the spare income!) although the executors will have to demonstrate that the deceased was not using up capital to do it.
Robert