This is a v interesting situation. The employer should have actually stated clearly that you were being dismissed due to redundancy, as redundancy is a "fair" ground for dismissal. I suspect that they didn't want to use the term "redundancy" so as to avoid paying statutory redundancy; which was unnecessary because you are not entitled to statutory redundancy in any case because you have less than 2 years' service. The two weeks' notice for redundancy only applies where you have this 2 years' service.
IF they had dismissed you due to redundancy (and stated as such) and IF your contract has no notice period, then giving you one week's pay in lieu of notice and letting you go would have been perfectly OK. However, because they have, in effect, dismissed you for no reason (you are inferring that it's due to redundancy), then, on the face of it, there's a claim for unfair dismissal. Obviously, if you bring this up, the company will turn around and immediately say that you are being dismissed due to redundancy so you'd be basing a claim on the fact that they flip-flopped on their reason for dismissing you. It does sound like they are actually dismissing you due to redundancy so, on the substance (but not form) of it, they would be in the clear. I personally wouldn't fancy taking a full unfair dismissals case on this basis but you may be able to use this info to negotiate an additional week's pay.
I'd recommend that you head to an employment solicitor to clarify but can understand that, for the sake of a week's pay, you may not want to. The remedy for an unfair dismissal is up to 2 years' remuneration, but I really can't see you getting anything like that even if you are successful. If you try to deal with it yourself, you may be successful in getting your extra week, but are taking that risk that they just stonewall you and change their tune to finally say that you were dismissed due to redundancy and, thus, have no unfair dismissals claim. If I was the employer, I'd pay you the extra week toot sweet and clobber whoever reckoned that being circumspect on the reason for dismissal was a good idea...