Wales, Scotland and Northern Ireland have variations on the law. Not sure why though.
In the case of Scotland, many of its laws were laid down and in place before the act of union in the 1700s and the legal system did not change. Under the law an English policeman can exercise his powers anywhere in England irrespective of which force he belongs to but has no power in Scotland (not sure about Wales). The same applies to a Scottish policeman, obviously.
Legal differences are quite marked. IIRC In Scotland you still can't be arrested witout a second policeman present to corroborate the eveidence of the arresting officer. Also we still have a verdict of not proven (a half way house between guilty and not guilty and not a particulary nice verdict to have haning over your - sort of we think you are guilty as hell but can' conclusively prove it). There are also differences in civil as well as criminal law. For example if you put an offer on a house and it is accepted by the vendor he is prohibited by law from accepting a higher offer (thus no gazumping). Also you are bound by law to follow through on the purchase and can be sued if you pull out at the last minute.