Getting There
NORWAY: BY AIR
From UK: direct flights to Oslo, Stavanger, Ålesund, Bergen and Trondheim from London and some regional airports, including Manchester and Edinburgh (for Oslo), and Aberdeen (for Bergen & Stavanger). Airlines include Norwegian, SAS, BA, Ryanair and Wideroe.
For Tromsø, you'll need to change planes - most likely in Oslo. Note that Oslo's main airport is Gardermoen, 45km north of the city, while the smaller Oslo Rygge and Oslo Torp are respectively 60km and 110km south of the city (on different sides of the Oslo fjord).
From the rest of Europe: flights from most capitals and some major cities to Oslo, and also to a few regional airports. For direct flights to Tromsø, options include Dusseldorf and Frankfurt (with Lufthansa or Eurowings) and Zurich (with Swiss).
NORWAY: BY TRAIN (& FERRY)
From UK: you can take the train from London all the way to Oslo, with 2 overnight stops (Brussels & Copenhagen) or possibly just 1 overnight (in Hamburg). For more info see Seat 61.
Or you can use a ferry for part of the journey, such as Copenhagen-Oslo (with DFDS) or Kiel-Oslo (with Color Line) or Hirtshals-Kristiansand (with Fjordline or Color Line).
There are currently no direct passenger ferries from UK to Norway.