I mean any filter with mechanical and biological elements. Doesn't matter if it's internal or external, although external would be better so that it doesn't take up any of the already very restricted space.
Really you shouldn't consider keeping a Dwarf puffer in a anything less than a fully cycled five gallon or preferably 10 gallon.
The whole set up should run you about 40 dollars or so for a good filter and heater, An american 10 gallon tank as is with nothing else is 8 dollars, I dont know the dollars to pounds conversion.. Good luck with the fish would be curious to see how it turns out.
its my experience that tank set-ups that cost X dollars in the US tend to cost X pounds in the UK. you're probably looking at ~50 quid for a brand-new 8UKg setup.