There is no limit as such but there are limits to how much can be gifted free of a potential Inheritance Tax charge. Take a look here and here for information on exempt gifts. If the £3,000 gift exemption is not fully used in one year, the unused balance can be used in the next tax year.
For those with large incomes, there is a gift out of income exemption. You can read about that here.
I hope this helps but let me know if you have any further questions.
For the avoidance of doubt, the recipient of a gift does not pay income tax or capital gains tax on it.