A swarm of relatives can claim a share of the inheritance as per Thai law if you don't prepare a will. There are 6 classes of statutory heirs in Thailand, besides a spouse. Children, grand children, parents, siblings, half-siblings, grandparents, uncles/aunts. Even if there are none on your side, the Thai court and your bank in Thailand are supposed to make a bureaucratic fuss before they transfer your possessions to your surviving wife - because they should have proof that no other claimants exist. An affidavit by your executor in the UK, even if he digs up birth and death certificates for your complete family tree, back to Lord Nelson, may not suffice. After all, you could have relatives in other countries. It could take years before they release the bank accounts to your wife. Of course, TIT: they may not bother to make a fuss if the potential relatives are foreigners. But I'd expect Thai courts and banks to not hand over your bank account without a heap of paperwork.
Worse, the niece of your wife would probably get nothing without your wife's written will.
You should register your marriage in both countries. After you or she dies, the UK, SG and TH courts will insist that the survivor proves her/his claims as spouse before they release the bank accounts. The paperwork will be about the same, but it will be easier and less expensive to get a national marriage registration certificate while both spouses are alive.
The second step is easy: Under Thai law, you can make a so-called holographic testament, hand-written in English (section 1657 Civil and Commercial Code). Mention it it that at the time of writing, you don't have any surviving relatives that could be statutory heirs. Your sole heir shall be your wife. This should speed up the release of your bank account to your wife. Put this hand-written will somewhere safe, where your wife can find it, and she should be able to have it recognized by the Thai probate court after you kick the can down the road.
She should write her own handwritten will to make sure that her niece gets everything (or anything) after her death. Or else, a mob of her other relatives in classes 3 to 6 could claim to be statutory heirs. Does she have siblings or half-siblings? I'm not even sure that nieces belong to the lowest of the 6 classes of heirs. If not, the niece gets nothing without a will. If no statutory heirs exist after the death of your wife and she leaves no written will, either, the Thai government would pocket all her Thai assets. Her UK assets would go to her majesty's coffers, the SG bank account to the SG government.
Safer would be a will according to section 1658 of the Civil and Commercial Code. Have a lawyer write it in English and Thai (5 - 10k Baht) and file it at your local amphoe office in the presence of 2 witnesses. The witnesses must not be heirs. The lawyer can certainly provide the 2 witnesses, himself and 1 other.
Forms Of Wills under Thai Law | Family Law (samuiforsale.com)
There are also Word templates you can find by Googling, with the text in both English and Thai, so the lawyer and/or you only need to enter the names. No expensive translation is necessary for such a standard text.
When you hire the lawyer, you may also consider to write a "physician's directive" or "living will".
“Section 12: An individual is entitled to make a Living Will expressing that person’s intentions to refrain from receiving medical treatment for the purpose of extending the last phase of their life or for ending the suffering arising from the illness.
Living Will in Thailand - Complete legal advice from professionals (isaanlawyers.com)