Most of the police units have a minimum twin engine time amongst others (e.g. total hours) specified in the operations manual - this is approved by the CAA according to the unit's location, type of operation etc.
There is a position in this weeks Flight mag which requires 500hr multi and 2000 TT, but some are less restrictive. I believe there has been some allowance made for experienced single engine pilots in the past(where there was no multi specified), but there may not be many positions without the multi requirement - obviously military/turbine/operational experience can be a big help.
There was a thread recently about the percentage of non-mil police pilots, can't remember the figures but there were definitely a few civvy all the way types....