I worked for MOJ and was made redundant a few years ago after approx 2.5 years service. All up I got 9.5 ish weeks payout, so it must have been 6 weeks for the first year, and 3 weeks pro rated per year after that or something.
This would be a pretty standard government clause as it was on a duplicate of the PSA contract.
Now with a private company (300+ staff) and we have something but not quite as good. It is 1 month for the first year, then another 2 weeks per year after, to a maximum of 52 weeks total.
3 months for the initial would be a lot, but 3 months flat isn't much if you are there for a few years. You should definitely do some kind of increasing payment. And make sure it includes to prorate the final (part) year of service.