I wonder if it's a crime to legitimately have to defecate publicly due to having diarhea? Anyone know?

Further to the previous reply to your question, I had a look at UK Bladder and Bowel foundation.
Although you may be uncertain about how an employer may react, there are good reasons for telling a potential employer about a disability, including continence. Employment is covered by the Equality Act 2010 (which replaced most of the Disability Discrimination Act). This means it is unlawful for employers to discriminate against disabled people in their recruitment and selection procedures.
Under the Act employers must also consider making any ‘reasonable adjustments’ you might need in order to enable you to work for them. Many people with bladder and bowel problems are covered by the Act (see our section on incontinence and discrimination or visit the UK Government’s website)
How do you decide when to declare a continence problem?
There is no easy answer. If you are applying for a new post it may be easier to declare on application or medical forms. If you are covered by the Equality Act 2010 it is unlawful for them to discriminate against you.
If you've got a genuine continence problem, it appears that you can't be issued a criminal conviction under the Equality and Discrimination act.