Movingonup You need to differentiate between gifts out of capital and gifts out of income.
Gifts out of capital
£3000 is the annual exemption in total. In addition the £250 small gifts exemption can be used for gifts to any number of people in a year but you cannot use that exemption more than once in the same year to the same. person. There are other exemptions for gifts out of capital (wedding presents for example) These are all gifts out of capital (ie your savings). These annual exemptions do not fall within the 7 year rule. However, if you were to give her £10,000 then that would be subject to the 7 yer rule.
In the example you give above the £250 for Christmas is a "small gift" out of capital. The £250 for her birthday must come out of your income. If you give her £3000 that is exempt but you cannot claim a further £3000 exemption for a second grandchild (or anyone else) in the same year.
Gifts out of income
You can give as much as you like in gifts out of income but they should be regular and out of income and not affect your standard of living.
7 year rule - if you are worried about this, keep a record of the date and amount of the gift and the beneficiary. Also give the beneficiary a letter along the lines of "Dear.... Please find a cheque for £10,000. Please keep this letter"
The same thing applies if you give away valuable furniture, jewellery or paintings, - keep a record.