Converting my Raleigh Equipe to a single speed: Can I use a conversion kit? I am a complete bike novice and am trying to convert my raleigh equipe road bike into a single speed (after a plastic bag blew out my rear derraileur).

I have purchased a single speed conversion kit: https://www.amazon.co.uk/gp/product/B01LWVTCS0/ref=ppx_yo_dt_b_asin_title_o06_s01?ie=UTF8&amp;psc=1 but have not been able to fit it onto my wheel.  

If I purchase a shimano cycling freehub (something like this: https://www.amazon.co.uk/gp/product/B00G98QQU0?pf_rd_r=H50JHNAAZCRQN6SV9FQM&amp;pf_rd_p=e632fea2-678f-4848-9a97-bcecda59cb4e), would I be able to attach it to my wheel, having removed the freewheel, so the single speed kit would work?

Photo of the wheel and removed free wheel attached.
No, you have a freewheel and the conversion kit you have bough is for a freehub. The freehub you have linked to will not fit your freewheel.   

I don't know if you can get freewheel kits with spacing.  Most freewheel kits I have seen have the cog close the hub flange - the chain line would be wrong on your wheel.