Subject to meeting Home Office regulations, each police force can determine its own entry criteria, so there's no fixed rule.
Anyone applying to join the police force has to declare all criminal convictions. Unlike applications for most other occupations, this includes minor motoring offences. It would then be up to the panel considering your application to decide whether they were relevant. (3 points for speeding a couple of years ago probably wouldn't matter. 9 points in the last 6 months, after just getting your licence back following a ban, probably would!).
If you're seeking further information about joining the police force, see here:
http://www.learndirect-advice.co.uk/helpwithyo urcareer/jobprofiles/profiles/profile170/
Chris