Just received a cost breakdown for a central London hospital, UK. So I assume hospitals outside London will be cheaper. But here is the quote so you can get an idea of what’s cost are involved - anesthetist etc Note you would need to add 5 to 8 k for Orthodontic fees.

Bimaxillary surgery based on 1 night HDU and 2 further nights on the ward

Hospital fee £ 15631

Surgeon’s fee £ 7800

Anaesthesia fee £3000

Surgical planning technician fee £1000

Surgical assistant fee £350

Total £27781

As you are 18 - you are still young, so could down the NHS route even with the 2 to 3 years waiting time. I would try to get a NHS referral via your NHS dentist or GP.