granny grump - The Money Mail gives you three date options. In fact the last silver 3-penny pieces for the UK were minted in 1941, they do not give you that option as an answer. So perhaps they are referring to the following link which does actually make a reference to 1945.
http://www.coins-of-the-uk.co.uk/three.html
''Although the silver threepence continued to circulate for some years and particularly in Scotland and the West Indies, it was last produced for circulation in the UK in 1941. Issues were made for the next three years for use in the West Indies, and are all relatively scarce, particularly the 1944 coin. Nearly 400,000 were minted in 1945, but the great majority were melted down - a very few, one or possibly two, have survived.''
Good luck