I have savings that had been invested or earned interest in a UK bank. When I bring this back into Thailand am I bringing in already taxed savings I earned in Thailand or am I deemed to be bringing in subsequent investment gain that might be taxable?

Fixed deposits are taxed on the capital gains that have been made and what percentage of the gains are remitted into Thailand. You will have to declare this on your tax return. There maybe tax credits available if tax has been paid in the other jurisdiction, depending on the DTA between that country and Thailand.