Wikitravel is an excellent source of information:
https://wikitravel.org/en/Vancouver
(NB: You need to click the links for each of the districts to get the full picture).
Vancouver International Airport is served by direct flights from Heathrow, operated by both Air Canada and BA.
Air Transat and WestJet operate services from Gatwick.
Air Transat also flies to Vancouver from Manchester.
(Note that the Air Transat and WestJet services, don't operate all year round though. They're classed as 'seasonal').
There are no other direct flights from the UK.
There are no direct flights between Stockholm and Vancouver.
Montréal is loved by many visitors. It would make a good second city to visit in Canada. (With its French language and culture, it's very different to Vancouver):
https://www.mtl.org/en
https://wikitravel.org/en/Montreal
Flights between Vancouver and Montréal are operated by Air Canada and Air Transat (both all year), as well as by WestJet (seasonally).
Flights between Montréal–Trudeau Airport and the UK are operated by Air Canada and BA (both year round, to Heathrow), as well as by Air Transat (seasonally, to Gatwick)