Cheapest would be to make your own using soft drinks bottles, air line tubing and a bit of yeast, sugar etc. There are some tutorials on here somewhere.
Fire extinguisher set ups are cheap enough in the long run and are more accurate and reliable than the former but the initial set up can be costly. You can pick second hand stuff up cheap enough though. Expect to pay over £60 plus the cost of the FE and that's at a cheap second hand price.
FE for sure.
I'd have a good look on ebay, normally a 2kg FE is around £20 (try and find one locally so you don't have to pay delivery).
The regulators start at about £20 for a basic on/off with one gauge, up to £300 with dual gauge, solenoid and PH controller.
If you can afford to get a solenoid I'd recommend it unless you intend to turn it on every morning one hour before lights on and off one before lights off, of equally you can leave it on 24/7 but won't be able to get high levels without gassing the fish.
After the FE and regulator all you need is some CO2 proof pipe, diffusers, bubble counter and none return valve (available cheaply on fleabay).
I managed to set up a FE setup for under £40 because I went after the bargains.
Here is what you need along with some links to ebay items.
A co2 source, usualy a fire extinguisher. http/www.ebay.co.uk/sch/i.html?_from=R40&_trksid=p4712.m570.l1313&_nkw=co2+fire+extinguisher&_sacat=See-All-Categories
A co2 gas regulator http/www.ebay.co.uk/itm/SWP-Side-Entry-CO2-Gas-Regulator-2-Gauge-Welder-Welding-Pub-Bottle-Beer-/140776182405?pt=LH_DefaultDomain_3&hash=item20c6ea1285
Some co2 proof tubing. http/www.ebay.co.uk/itm/Rhinox-CO2-Proof-Tubing-Live-Aquarium-Plant-Diffuser-SI-/250445502160?pt=UK_Pet_Supplies_Fish&hash=item3a4fb716d0
A non return valve. http/www.ebay.co.uk/itm/2x-Aquarium-NON-RETURN-Check-VALVE-for-air-pump-airline-/270668494505?pt=UK_Pet_Supplies_Fish&hash=item3f051976a9
A drop checker & reagent to go in it. http/www.ebay.co.uk/itm/CO2-Drop-Checker-with-PH-solution-check-co2-level-UK-SELLER-/221047964284?pt=UK_Pet_Supplies_Fish&hash=item33777c427c
A bubble counter (I dont use one but a lot of people do) http/www.ebay.co.uk/itm/FLUVAL-Co2-BUBBLE-COUNTER-88g-/310409015219?pt=UK_Pet_Supplies_Fish&hash=item4845d1afb3
A co2 diffuser http/www.ebay.co.uk/itm/Glass-Co2-Nano-Diffuser-Aquarium-Fertilizer-UK-Aquatic-Plants-Like-Dennerle-JBL-/230796352025?pt=UK_Pet_Supplies_Fish&hash=item35bc88da19
That is for the basic set up, but it will mean that you will have to turn it on & off by hand every day.
If you want that bit automated you will need a solanoid valve. http/www.ebay.co.uk/itm/CO2-Magnetic-Solenoid-Valve-for-Aquariums-0-0-8mPa-/350481860748?pt=UK_Pet_Supplies_Fish&hash=item519a58c88c
Ther you have it, add up the costs to give you an idea of inital outlay, but once purchased all you will need to do is replace your co2 supply when it runs out.
A lot of those listings are from abroad, but I did a very basic search. Take your time there are bargains to be had.
There are many regulators on that site you mentioned so please don't pick the first one you see. Contact the seller and ask if they'll fit.
I also got mine for £50 off a member on the forum here but I know I got it cheap.
Yer you want to make sure it says its suitable for UK fire extinguishers or pub-bottles. For £15 you can get a standard regulator without gauges just a simple needle valve or for £50+ you can normally get one with pressure gauges and solenoids, all depends on your budget.