I have assisted several Thai widows of British expats. They all receive the Personal Tax Allowance (currently £12,570), and this is sorted by the former employer of husband when paying the widow's pension. No need ever to deal direct with HMRC re the allowance
However, depending on the date of death of the husband, a tax refund can be claimed (sometimes automatic after a year or so has elapsed)
Note that the UK state pension ceases upon death. There are no longer any benefits for widows or children, nor the one off lump sum payment (was £2,000).................unless husband and family happened to be in the UK at time of death