You will need to show both Passports to the Staff at Check-in and later at Boarding because it is their responsibility to ensure that the passenger can enter the UK when the flight arrives there.
At Thai Immigration at the Airport, they will only need to see a Thai Passport - very rarely does Immigration ask to see a Visa for the destination Country or some evidence that she could enter UK, it's not their job, all they are checking is that the passenger was in Thailand legally - which a Thai Passport obviously proves.
It's not a good idea to show Thai Immigration both Passports - as I say they just need to see the Thai one and showing them 2 will only confuse them. Some Officers may not even know that it is legal to have 2 Nationalities and cause problems.
Always enter and leave Thailand on the Thai Passport, if she uses her British Passport she is limited to how long she can stay without getting a Visa extension or whatever.
Patrick