It looks like you might have to stick with Ryanair (unless you're prepared to travel via Gothenburg- see below). I've checked the websites of all the international airports in Sweden. Here are the results:
The only scheduled flights from London to Stockholm Skavsta are with Ryanair from Stansted.
The only scheduled flights from London to Stockholm Arlanda are with BA (from Heathrow) and SAS (from both Heathrow and London City).
The only scheduled flights from London to Stockholm Vasteras are with Ryanair, from Luton.
The only scheduled flights from London to Malmo Sturup are with Ryanair (from Stansted).
There are no UK flights to Mora Siljan, Karlstad or Gothenburg City.
Gothenburg Landvetter is the only airport which offers a choice of budget airlines flying from London. As well as Ryanair's service from Stansted, there are flights operated by FlyMe (also from Stansted):
http://www.flyme.com/en
(FlyMe also operate from Gothenburg Landvettter to Stockholm Arlanda so it might be possible to combine cheap flights).
Chris