How much time are you planning on spending here? And do you want to visit a couple of places and really get to know them or do you prefer hitting lots of places and seeing the one or two main tourist sites?
Realistically, it is impossible to visit Canada, unless you are here for a year or so. The country is vast!
Since you are flying from the UK, it is likely you will land in Toronto, Montreal, or Vancouver (about 2 hours longer flight).
I have not toured Montreal, but it is considered the European-style city in Canada. Lots of Quebec/French culture, cafes, bistros, etc. Should be fairly warm in the summer.
Toronto is the largest city in Canada, the business centre, and as far as Torontonians are concerned the centre of the universe! Should be sweltering hot in the summer. I spent a few weeks there in July and I could barely leave the house during the day due to the humidity.
Vancouer (where I live) has a lot of outdoorsy stuff that is available right from the city. There is skiing (even in summer) at Whistler-Blackcomb, a little over an hour's drive north. There is lots of hiking and walking right in the city and the suburbs, and there is serious hiking on the North Shore mountains again, only a few minutes from the city centre. There is also water sports on the ocean. The weather should be warm to hot, although rarely humid. And it can always rain!
I should also mention Ottawa, which is located between Toronto and Montreal. As the national capital, it has the greatest concentration of museums and such in the country. If you are here for July 1, I would recommend trying to attend the Canada Day celebration at Parliament Hill. The one day a year that Canadians become flag-waving nutbars!
Of course, there are absolutely hundreds of other places to visit, Gros Morne National Park in Newfoundland is supposed to be spectacular. Drumheller in Alberta has some serious dinosaurs. The beaches and golf on Prince Edward Island are amazing. Quebec City has some great history as well as food and true Quebecois culture that is worth visiting. The aforementioned Banff/Jasper parks are beautiful too, although often overrun with tourists in the summer. And then there is the north...
If you are here for only a couple of weeks, I suggest choosing one place, and spending your vacation there, and really get to know it.
Have fun.
