Next time try bottling instead of using the pressure barrel. That's probably the main culprit (CO2 leak). I'm assuming you're in the UK as almost no one uses those in the states. Homebrewers in the US almost all use capped or corked bottles or cornelius kegs, which will also work fine with a good seal (for which you probably need a CO2 tank). I can understand wanting to use the pressure barrel to get the cask experience though. I don't own one, but with kegging, you can lose CO2 if the seal is leaky. They make petroleum-based, food safe keg lube that you put on the rubber O-rings for corny kegs - you might also try that on your pressure barrel. But bottling is probably your best bet. You could also go to the store that sold you the barrel and ask them for tips on sealing it.
Assuming your pressure barrel is plastic - did it ever swell and get taut? You should have enough beer in there so that there is not a ton of headspace. Then the CO2 will fill up the head space and be forced to dissolve into the beer. Once it the barrel swells, you could spray the seals with soapy water or star san and look for bubbles to detect leaks. If it never swells and gets taut, you probably have a leak.
The temperature could have also affected things - if the temp is too low, the yeast could go dormant. Ale yeasts are generally ok in the 60s, but below that you might have trouble.
Lastly, a level teaspoon of sugar per pint is not the best way to carbonate. You should use a carbonation or priming calculator - there are many online and they are in any good brewing software package. You calculate based on the volumes of CO2 desired for your style (e.g. 1.5-1.7 volumes for bitter). But you generally want to dissolve your calculated amount of priming sugar in boiling water and cool it before adding it to the beer. Boiling will sanitize, remove some oxygen from it, and having it in liquid syrup form will ensure that it dissolves much more evenly than adding solid sugar, as table sugar dissolves better in hot water. Once in liquid form you can mix or shake it in to ensure even distribution, but avoid agitation and exposing it to air as much as possible. Refer to Palmer's How to Brew (or better yet buy the book).