Will leaving Thailand on the expiry date of a retirement visa cause issues when re-entering with a new dependent visa?

First of all, you cannot apply for a visa from an embassy if you are in Thailand. You must physically be in the jurisdiction of that embassy in order to apply there. The visa application very specifically asks for your actual location and proof that you are there. So any application submitted would be fraudulent if you're not in the location.

Second, you said he has 1 year visa, but is he on an actual VISA or is he on an extension of stay? A visa cannot be cancelled, but an extension can be. For a retirement extension, there's nothing to cancel. You just leave Thailand without a re-entry permit and it will be invalid when you clear passport control.

Which country are you currently in? If you are in thailand you can't apply for a visa through the London embassy unless you are in the uk? If you are in thailand then unless you are planning on coming back to the uk. You will need to apply in a neighbouring country and use your entry stamp in your passport to show you are in that country. Go to Vietnam for example apply on their evisa system stay until you are approved.