Cannot install latest Security Update. Believe because system reserved space too small

[TommyT3]

My Bios is  Version/Date AMI F.30, 03/11/2017.

I belive this is why the latest Windows update fails - system reserved  allocation is only 260MB. I am trying to install a later version of the BIOS. 

I followed the Instructions and got "Installation completed" - but BIOS is still the old one.

[TommyT3]

To expand on what I have said: My PC is a System Model HP Slimline Desktop PC 260-a160na.

When I enter the details and go the Driver Update page, I am told that all my drivers are up to date. However, when I expand the list and click on BIOS, I see 3 versions listed - all later than mine. It is not clear which I should choose since the one with the highest version number is not the one with the latest release date.

I picked one at random and downloaded it successfully. I inserted a flash drive as instructed and files were copied  to it.

I did a reboot with the flash drive inserted but the old BIOS is still there.

Why am I told that there is no update available when it appears that there is?

How do I pick the correct one of the three listed?

How do I get it to install?

[TommyT3]

OK so I have realised that only one of the 3 BIOS upgrades available is for my motherboard. I selected the right one and it has installed correctly. Progress! But why did HP inform me that I already had the latest version of everything?

However... the size of the system reserved partition has not changed. It is still 260MB. and the latest Windows update still fails.

I still think that the problem is that the system partition is too small - do I mess around with third party software to increase it??