Budgetair — Flights Unuseable

Booked through Budgetair 2 return flights to Milan from Newcastle, flying with Ryanair.
Booked on 4 August.
Received Booking confirmation from Budgetair and itinerary from Ryanair
Had to verify my identity via Ryanair website. They could not find my booking. Called Ryanair they said the email address associated with my booking was not the email address I had used to book.
Contacted Budgetair – they insisted it was, and that I contact Ryanair.
Contacted Ryanair again – they told me they could not access my booking with the information I had and to contact Budgetair.
This went on and on in a loop of multiple emails. No-one resolved the issue and I am still unable to verify my identity, so cannot use the flights, without paying a fee at the airport.
Had to book new ones. Attempting to get a refund from Budgetair – they are not assisting and still insisting I contact Ryanair. Which I have told them on multiple occasions that I can’t do.