Airports

There are several options to fly here;
Stansted to Ljubljana with Easyjet
Ljubljana is around 90 minutes from the venue

Stansted or Birmingham to Trieste with Ryanair
Trieste is less than 1 hour from the venue

Stansted to Klagenfurt with Ryanair
Klagenfurt is around 2 hours from the venue

Various UK airports to Venice (Marco Polo)
Several carriers operate this route. It is around 2 1/2 hours to the venue. You can then get a train to Gorizia where you are then just 60 minutes from the venue.

Bristol to Treveso with Ryanair
Treviso is about 2 hours to the venue by hire car. You can then get a train to Gorizia where you are then just 60 minutes from the venue.

Easyjet is probably the prefered for a local flight at a sensible price.
Ryanair will likely be the most expensive carrier (with Sports kit), but get you to the closest airport.

Notes (when I last checked):
BA = 25kg main luggage. Unlimited hand luggage
Easyjet = 20kg main luggage. Unlimited hand luggage. 18 GBP Sports kit (each way)
Ryanair = 15kg main luggage. 10kg hand luggage. 40 GBP Sports kit (each way)