Blondiescot
It used to be very common for people to state in their will that they wanted their jugular vein to be severed by the undertaker - just to make absolutely sure that they were dead!
And I know I've said this on other threads on a similar topic, but if you've given instructions that you want your body to be donated to science, you need to have a Plan B in case they won't accept the body. This can happen for any number of reasons - they may already have their full quota of bodies at the time - as happened when my mum died.
I don't think you can just say you want to donate your body to science without planning this well in advance.
As BlondieScot says, they don't accept everyone.
My FIL wanted to donate his body but didn't organise this so it didn't happen. He was cremated.
There was a TV programme on a while ago about two people suffering from terminal cancer who had been accepted to donate their bodies to medical science. The programme interviewed them whilst they were alive and it followed through to how they were used for medical science. The gentleman was preserved in formaldehyde used by medical students to learn about the body generally. The lady was frozen and used for doctors to practice hip replacements. Once defrosted the body had to be used within three months.
A few months later, the hospital arranged a memorial service for all of the people who had donated their bodies over the previous few months. The family members attended and there were photographs of the people who donated.
Sorry if it all sounds a bit morbid but the process of medical donation was something I was not aware of until seeing the programme.