Qatar Airways - denial of boarding by airlines

Me and my co passenger were cleared by visa approval by the UK immigration for appearing for exam for Fellowship of Royal college of radiologists(FRCR). We booked flight to London Heathrow airport from Chennai international airport, round trip from Qatar airways. Booking reference SARTWZ and SBG*D*, Flight numbers QR *** and QR *** with transit in Doha. Date of departure ** August ****.
We had all documents as cited in the website of UK government and immigration rules for travel from amber list countries(India on **/**/****), Qatar airways, Qatar transit rules and government of India. We had predeparture RT PCR negative results, passenger locator forms, booked tests for day * and day * and arrangements for self isolation at rented home. However Qatar airways denied boarding claiming that "UK immigration and borders required us to be fully vaccinated for entry into UK from India and repeatedly blamed UK immigration and border at Doha and London for denying us boarding and it is not the fault from the part of Qatar airways". However UK immigration laws clearly state that Indian vaccines are not approved in UK as of now and vaccination status from India is irrelevant to UK immigration. We have attached all relevant documents supporting the same.
This created severe mental, physical and monetary stresses to us and we had to book a last minute flight from another airlines(Air India). We were cleared easily at the UK immigration and we verified that UK immigration had no role in our predicament. Hence we hold Qatar airways responsible for the mental, physical and monetary stresses we had to go through and the impact it had on our performance in the exam and thus our career. As the tickets were round trip, Qatar airways cancelled our return tickets as out of series at the last minute of boarding from London Heathrow airport.
We require complete refund and compensation for our losses and difficulties that were caused.