The 50 pence pieces that are not part of a set can be single year issue commemorative coins such as the very well know Kew Garden 50p which was issued in 2009 to celebrate the 250th anniversary of the foundation of the Royal Botanic Gardens. This coin is currently the rarest design with 210,000 coins created to enter circulation. It has received a great deal of media and hype which has led to increased demand and therefor price of this coin.
It is worth noting that there have been rarer coins in terms of numbers entering circulation, for example the no longer in circulation UK Council of Ministers Presidency and completion of the Single European Market coin had just 109,000 coins enter circulation and without the press coverage and hype, does not achieve values reached by the Kew Gardens coin. (Although Kew is of course a prettier coin with a better subject matter). The Kew coin was also produced as part of many collector packs in Brilliant Uncirculated (BU) condition, so the actual number of coins bearing this design will be much higher than 210,000 when these are included. For example, the 2009 Baby Gift Set with a run of 50,000 units included this coin.
The two 50 pence coins that make up the vast majority of coins in circulation today are Britannia (1982 to 2008) and it’s replacement Shield of the Royal Arms (2008 on).