Dizzi,
For small precision tools I suggest you buy a "Bisley" paper storage cabinet made of steel with drawers about 2" deep. They are available in e.g. 5, 8 10 15 etc. drawer units . They are a very good second hand buy from used office furniture dealers. I still have and use a 5 drawer version purchased many years ago before I could not afford a genuine toolmakers chest.
Wooden chests are constantly advertised on eBay but good ones make silly money however ones with a little damage can go for more reasonable amounts.
Car boot sales are a very good place to find both toolmakers cabinets and Bisley paper draw units.
Machine Mart sell new Chinese ones that should serve very well at about £131 or if you look out for their VAT free days £109.
Full size filling cabinets are not much use in a small workshop as the drawers are too deep meaning that small items would need to be pilled on top of each other.