It is true. After passing through the house of Commons and Lords, she has the final say - the "Royal Assent."
But that's not what you originally said; you said:
The Queen has to sign every law
...which isn't true, and hasn't been since at least the middle of the nineteenth century (when the Clerk to the Parliaments started to add his signature to authenticate them), and probably not since 1497.
And we* shouldn't forget that Royal Assent is normally granted by the Lords Commissioners acting on behalf of (and therefore not bothering) HRH, and that - thanks to the Parliament Acts of 1911 and 1949 - some Bills can be presented for Assent by the Commons without being passed by the Lords.
It's also the case that Statutory Instruments - which are just as much law as Acts of Parliament - require no Royal Assent at all.
Anyway, to try to get this back on-topic, by a strange coincidence the last three times any significant questions were raised about the constitutional status of Acts passed be Parliament were:
British Railways Board v Pickin in 1974,
Edinburgh and Dalkeith Railway v Wauchope in 1842, and
Lee v Bude and Torrington Railway Co. in 1871. I'll leave the fun of looking up the case details to you!
* - not the Pluralis Majestatis
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