OK, long version..
In the header of the Airbnb T&C’s https://www.airbnb.co.uk/terms Airbnb lists the ODR as a dispute resolution provider, it says “You can access the European Commission’s online dispute resolution platform here: http://ec.europa.eu/consumers/odr.” So thats one option open to you.
Then in the Payment Terms section it states that Airbnb is a payments service provider:
https://www.airbnb.co.uk/terms/payments_terms
1.1 Airbnb Payments provides payments services to Members, including payment collection services, payments and payouts, in connection with and through the Airbnb Platform (“Payment Services”). Please note that “Payment Services” include Airbnb Payments services associated with free Listings provided through Airbnb’s Open Homes Program.
So for this reason the Financial Complaints Ombudsman should be able to resolve a payment dispute too. Airbnb Ireland is a UC, (not an LLC as I thought earlier - different country!) and all Airbnb hosts outside of the US and China transact through Airbnb Ireland UC.
The EU ODR (Online Dispute Resolution) platform only applies to EU hosts obviously, (and not China) and UK hosts can use this resolution until Jan 1 2021 because of us leaving the EU.
Otherwise, arbitration complaints can be taken through AAA (American Arbitration Association), again, as per Airbnb's T&Cs.
@Tim2309 You can request all communication you've had with Airbnb in relation to your issue to be released under The Right To Access, as laid out in the Data Protection Act 2018. You should be able to email Airbnb here: dpo@airbnb.com to get that.