The Royal Mint advises that 129,644,000 Sixpences were issued in 1965 making it easily the most issued, if not used coin, in 1965.
In 1944, the British used Pounds, Shillings and Pence. The British have never used cents. There has never been a British 10 cent coin and the British 10 Pence coin was first issued in 1968.
The Royal Mint did not produce a 1965 rhodium plated 24 carat gold Churchill Commemorative coin. Any such coin would most likely have been privately minted and would only achieve the value of the metals used, maybe a little more.
The coin is called a "50 Pence" coin. The term "50 New Pence" was last used in 1981.
The Penny is used the most in the US.
Any coin with two dates on it, 200 years apart, is a commemorative. The British 2 Pence coin has never been used as a commemorative, but the 2 Pound coin has. The British 2004 Two Pound coin commemorates the 200th Anniversay of invention of Trevithick's locomotive.
Until about 1965 Australia used the British pound.
The 1983 One Pound coin was the year of first issue for the British One Pound coin which replaced the One Pound note. The British One Pound coin is legal tender anywhere in the United Kingdom and some of its dependencies.
You do not specify the denomination or the country of origin, but no 1966 British general circulation coin with the legend "Elizabeth II dei gratia regina fd" contained any silver.
A British Caribbean Territories 1965 bronze 1 cent coin (Elizabeth II), uncirculated and in absolute mint condition could fetch up to £0.50 GBP. If it has been circulated, not much. The values quoted are the best possible for the best specimens in their grades, but may be significantly lower due to varying demand for the coin and the prevailing economic climate. A reputable coin dealer will be able to give a more accurate valuation based on inspection of the coin.
Your coin is worth face value only; hundreds of millions were minted. Note that the coin is simply a 1965 dime, not 1965-P. The P mint mark wasn't used on US dimes until 1980, and no US coins of any denomination had mint marks from 1965 to 1967.
No U.S. coin dated 1967 will have a mintmark, they were not used from 1965-1967.
Such a coin does not exist. Canada has not used the British sterling currency system since the mid-19th century. If the coin has no country name on it and has a sailing ship on the reverse, it would be a British Halfpenny.