The only source of reliable information regarding the actual marriage ceremony (and the associated paperwork) has to be the Finnish Embassy:
http://www.finemb.org.uk/en/
Levi is served by Kittil� Airport (15km, 9 miles). The airport's website
http://www.ilmailulaitos.fi/airport_kittila states that the only scheduled airline using the airport is Finnair. (Although there are also [expensive] air taxi services available).
The Finnair website shows inclusive return fares from Heathrow from �291 (with long waits in Helsinki) or, if you've found some cheap flights to Helsinki, Finnair can get you from Helsinki to Kittil� for 133 Euros (about �93) return:
http://www.finnair.com/
If you need to sort out some accommodation, then contact the Finnish Tourist Board in London. Their web site is here:
http://www.visitfinland.com/web/uk/index.nsf but you'll probably need to phone them: 020 7365 2512
Hoping that this might help,
Chris