There are no Income Tax implications on the receipt of a cash gift unless the cash gift generates interest or dividends. These would then potentially be subject to tax.
Further guidance can be found here (https://www.gov.uk/apply-tax-free-interest-on-savings and https://www.gov.uk/tax-on-dividends).
Inheritance Tax is only due when a person's estate is worth over £325,000 when they die, or if the person who died gave away more than £325,000 in gifts in the 7 years before they died. In this scenario the person in receipt of the gift within those 7 years will be liable to pay inheritance tax.
Gifts made in the last 7 years use up the £325,000 tax free allowance first, but if the gifts received are less than the £325,000 inheritance tax free allowance, any unused threshold can then be used by the estate of the person who has died.
If the person who died owned their home (or a share in it) the tax free threshold could be increased to £500,000.
The rules on giving gifts and the potential inheritance tax implications. can be found here:
https://www.gov.uk/inheritance-tax/gifts
https://www.gov.uk/guidance/work-out-inheritance-tax-due-on-gifts
