The Birmingham Mint, a private coin producer founded in Birmingham, UK, in 1794, turned out currencies for more than 100 governments as well as coin blanks, collector medals, and tokens for the vending industry. In 2003 the BBC published a piece 'The Birmingham Mint Goes Bust.' That's too bad.
The mint produced several modern sets of gorgeous coins and sold them to collectors worldwide. Often these came carefully packaged and displayed. You can find them on eBay and other Internet auction sites.
The value of these coins is a combination of (1) bullion value and (2) sentimental value. Bullion value is usually easy to determine, but sentimental value can range from zero to sky-high. A jeweler can often help determine bullion value.
To compute bullion value look at the coin and its documentation. You cannot go by the coin's appearance, as some silver- and gold-looking coins are made of base metal. Find the weight of the coin and multiply by fineness to get the bullion content. For instance, a coin that weighs 45 grams and is made of sterling silver contains 0.925 x 45 = 41.6 grams of silver, because sterling silver is 92.5 percent fine. Convert the weight to troy ounces: 41.6 grams = (41.6 / 31.1) = 1.34 troy ounces, because there are 31.1 grams per troy ounce. Finally, look up the price of bullion on the Internet. Today's silver price is about $12 US dollars per troy ounce, so the bullion value of the 45 gram sterling coin is 1.34 x 12 = $16 US dollars.
If you take your Birmingham Mint coin to a collectibles dealer, he or she will consider sentimental value equal to zero. The offer you get will be somewhat less than bullion value. On the other hand, a collector who enjoys nice looking collectibles may pay twice bullion value to buy your coin. It all depends on who you are selling to.