The info says:
The estate doesn’t pay Inheritance Tax on up to £3,000 worth of gifts given away by the deceased in each tax year (6 April to 5 April). This is called the ‘annual exemption’.
However, my mother's gifts were £5,000 per year, so over the UK threshold, but under the US threshold. My tax home is the UK.
The excess of each gift over £3,000 would have been a potentially exempt transfer. Where all or part of a £3,000 exempt gift allowance isn't used it one tax year, it can be carried forward one year so there is potentially £6,000 of exempt gifts that can be made in the later year. If the gifts were made from outside the UK, then they would not be caught by the UK IHT system in any event, assumibng your mother was not UK domiciled.None of the above affects your personal tax situation.