sloppyness is indeed the plastic housing you have identified. it will be a dealer only part so probs just as easy to call them up and ask for the part rather than part number I wouldnt worry about it too much. a decent parts desk should know what you are on about as its not uncommon.
as for the stiffness, this is more a service issue and doesnt really require any parts, just take the battery and tray off and grease the pin.
I found that even even after I had greased my pin on my recently purchased JTDm 16v it took a few days for it to really come good again as the grease worked in.
let me know where it is you find best for your parts wont you, as I'm based in Lincolnshire as well and don't have a local dealer for parts!
1999 156 1.8TS Sport Pack 3
2001 166 3.0 V6 24V Super
2003 156 GTA 3.2 V6 24V
2005 156 1.9 JTDM-Jet Sport
2008 159 1.9 JTDM Lusso
1997 GTV 2.0TS Lusso
2001 147 1.6TS Lusso