OK. Sorry, this is going to be a long one...
There are a number of possibilities as to what has happened.
- When they were recruiting they knew the role itself was permanent but they didn't want to get tied in to someone immediately in case that person didn't work out, so went into recruitment process with the mindset that it would be a contractor job, but then when they were interviewing you they were pretty sold on your skills and quite possibly forgot that they originally intended to couch it as a temp-to-perm when they instructed HR to take you on, so HR simply processed you as a perm hire.
- They told HR to make it temp-to-perm but HR messed up
- Somewhere in interview process they may have got their wires crossed and thought you had insisted on it being permanent as one of your conditions of joining, so processed you in as a perm member of staff.
Errors in themselves don't give you the right to be a permanent member of staff, but usually in a contractor relationship there is a 'pay-off' so that both parties benefit from the contractor relationship - both sides get the flexibility of being able to exit the relationship easily, the contractor loses lots of standard rights in the case of dismissal, and the contractor is paid a higher rate than the norm for a permanent role. That ensures it all balances out. If however all the benefits are on one side only (ie the company can decide they made an admin error and can get rid of you on a whim, but you have a 6 month lock-in on your side) then a tribunal may take a line against them and decide that in this case they treated you as perm, your contract suggests perm and therefore you were pretty much perm and should be protected as such.
If you are getting clear contractor benefits (IE - clearly higher pay than a perm would get) then the tribunal may instead take the view that you were indeed a contractor despite the documentation.
Given that you have only been there 2 months, if they come back to you saying this is an error, very sorry, there's not much you can do. And I imagine if it is an admin error then it will be flagged at the 6 mth mark - your manager will be asked by HR if you have passed probabation (to which he could well reply 'what probation?') - again if that happens there isn't really a lot that you can do. Whether a contractor or not, they can get rid of you within the first 12 months anyway, so your only course of action is to try to persuade them that they may as well make you perm there and then.
If however the 6 month mark passes and they say nothing then it puts them in a difficult situation should they then try to let you go saying you are a contractor because they will have triggered an 'end of probation review' so the tribunal will probably be persuaded that you were quite right to assume you were perm. - the company would have to convince the tribunal that their HR dept was really shit, and even then the tribunal may decide that that fact is their problem, not yours.
If you want to stay then I would not mention it at all, and certainly not before the year is out - simply because anyone can get fired in first 12 months. And once you go over 12 months there is even less reason to mention it as it would be normal for all sides to assume you are now perm.
Final thought - is there a company pension scheme? That would be a pretty good indicator to a court of your status.