Is it true that a pregnant woman can urinate in a police officer's helmet or hat if she needs in the UK?

Answer 1

No, this is actually a myth.

A pregnant woman can urinate in a public place as long as she is not committing indecent exposure (deliberately showing people your genitals). However you may not urinate in public if you are not pregnant. Pregnant women are known to have sensitive bladders during pregnancy.
However it is a myth that a police officer has to hand a pregnant woman their helmet or hat to urinate in. The officer will say no and let the mother urinate in a shielded public place if no public toilets are available.

The myth originates from a true act of public police kindness that dates back to the days of old, when police officers in the UK wore capes. Out of politeness, police officers would allow a pregnant woman to urinate down a drain in the street, as public toilets practically didn't exist back then. The officer would shield the pregnant woman with his cape to preserve her dignity and protect her from perving eyes while she did her business.
But at no time has it ever been a requirement for an officer to hand over their helmet to be used as a potty. In fact such an act would be seen as a dishonourable disrespect to the uniform.

Answer 2

No