When I joined, over 50 years ago, the height limit for most police forces in the UK was around 5'10'' with 2 or 3 requiring candidates to be 6'0''. It was necessary in those days for police officers to be large persons as we lacked the excellent equipment which today's officers are issued with to defend themselves or summon assistance quickly and frequently had to depend on our physical prowess to carry out certain aspects of policing.
However, things have moved on and given the kit which today's officers are issued, physical prowess and appearance are not as necessary as they were at one time. I see many officers on the streets today who are les than your 5'8''. Good luck.'