No, I don't think all authorities give the same days - my boyfriend gets something slightly different from me in neighbouring councils - we have a privilege day each at Christmas and Easter, although the one at Christmas isn't really a choice because unless you're in a service which has to function over Christmas much of the Council is closed anyway. And one extra day "in lieu of May Day" which doesn't have to be in May but does have to be in the right leave year.
I think national terms and conditions for local authority is 4 weeks + bank hols but different authorities also have slightly different terms in relation to extra days for those on higher grades or in some cases, all staff, or long service leave, and privilege days as mentioned above. Eg I get 3 extra days on scale 6 but if I was scale 5 or below, I wouldn't get those, and 2 extra for having worked for my employer more than 5 years, with another 3 if I stay there for 10 (that would be May 2008 for the year from May 2008-May 2009).