How can I report a death at the UK embassy in Thailand?

The police should do it really. Check with them first

Just call them, it can all be done over the phone.

The hospital can email/fax supporting documents.

I did this for my brother-in-law a couple of years ago.

She will also be entitled to a £2,500 on time payment from the British Government for loss of spouse, this is received by contacting the revenue department in UK.

Also check his pension, if he had one, she should be entitled to a percentage of his monthly pension.

Again, I say, I did all of this a couple of years ago, my sister-in-law still receives the monthly pension payments.

Phone them on Monday!

And to support the wise advice of cal them, this page has all the numbers

It take a long time if you try to use the website, but I hope I found the beginning of a report:

Talk to the British Honorary Consul or contact Lanna Care Net for advice.

call them - they will explain you what to do -