Your child should be allowed to own two passports in such situations, but a lot can depend on the attitudes of the two nations concerned. The British Government would have no objection, but the Thai government might.
The Japanese for example, only allow dual nationality until the age of 21, when a person has to decide which nationality he/she chooses to be.
In the case of my two daughters, who have a French father, they have always chosen to hold French passports as opposed to British. Apparently, the only problem they would have had with French authorities if they had held both was an inability to stand for high political office in Britain whilst retaining dual nationality and a French passport.
May I suggest you contact the Thai embassy on the matter and let us know how they respond.