I don't think so, you have very very very little rights to with hold rent.
Letter sounds fine, but in reality I have no idea.
I was told that if you withhold rent because of a fault they can start eviction proceedings against you for withholding rent !

I am not sure if this is correct but it is what they told me as I asked if I would receive a rent reduction to compensate for living with no landing light, no smoke alarm, and a hole in my ceiling for weeks (which is now 7 months, though the light now works again) and she said that its not somethign theywould reduce rent on, they have no obligation to fix the smoke alarm, and that if i witheld rent they could start eviction proceedings. (i didnt even mention witholding rent i just asked for a reduction that month to reflect the inconvenience)