Hi Tom,
This is my third year canoeing, before that I had never been in one. You will not regret getting a canoe, it is my favorite way to camp. I almost never go without it.
First, what is a Canadian Canoe? Here in Canada, we just call them "Canoes."
(j/k)
For 250-300 quid, you won't find much. You will definitely have to go used, and I have no idea what the market is like over there for them. You have to be careful, because it really depends on what kind of canoeing you will be doing. If you plan on doing some tripping, then you really have to watch the weight as you will probably have to portage it from lake to lake. Some of the cheap plastic boats can weigh upwards of 80-90lbs. You're best bet is to find a used but quality fiberglass or "royalex" boat. Fiberglass used to be the go to material, but few companies are even offering FB versions anymore. It's easily repairable but it requires repair if you're smashing into rocks, etc. If you get one from a good brand, you're looking at 50-70 lbs depending on the boat. Royalex is a plastic type of material. It is plastic layers and foam buoyant layers in between them. This is the new standard material for lower end canoes from quality manufacturers. It is bombproof.
I have a 16' Nova Craft Pal in Royalex Lite and it weighs 58lbs. I personally would not want a heavier boat. Mine is covered in dents and scratches. They are battle scars. As a beginner paddler, I highly recommend royalex if you can find one.
As for size, 15' is a perfect size for a tandem boat that will be used mostly for solo. I have a 16' and currently this is the same purpose I use mine (until my Fiance and I live in the same bloody place). I've paddled a 17' solo, and it's just too big. 14' would be ideal for solo, and can seat two people usually, however probably not two people and gear. Most canoes have capacities listed on their websites too. For instance, mine is 800lbs. More than enough for two big dudes and gear for a week.
You also have to look at the type of water you want to paddle. Are you planning on doing big calm rivers, whitewater, calm small lakes, big lakes, etc. Like anything, each canoe is special to a specific task, but can be used for others, just not idealy. I'll use two classic canoe designs as an example: The Prospector and the Pal (both used by Bill Mason). The prospector has a lot of rocker, meaning from front to back it has a lot of curvature vertically (looks like a banana kind of). This makes the canoe very easy to turn/pivot, but then also harder to keep in a straight line. It also has relatively high sides. Both of these features make it a good river tripping/whitewater canoe. On flat calm lakes, it obviously takes more effort to keep straight, and the higher sides can catch the wind easier. The Pal has little rocker, with a long flat bottom and 2" lower sides. This means it holds a line really well, is less effected by the wind, so its a great lake canoe. However both of these canoes can be multi use, just not as ideal at everything. I had my pal out in whitewater for the first time a few weeks ago. While I got a little wet, and couldn't spin around as fast as the other guys, I still had a blast.
I would advise, trying to save a bit more money to get a good canoe. It will be like a new best friend.