No, or at least not in all cases. This is because the timeshifting exemption applies to "broadcasts", which has a specific definition in the Copyright Act
(1) In this Part a "broadcast" means an electronic transmission of visual images, sounds or other information which--
(a) is transmitted for simultaneous reception by members of the public and is capable of being lawfully received by them, or
(b) is transmitted at a time determined solely by the person making the transmission for presentation to members of the public, and which is not excepted by subsection (1A); and references to broadcasting shall be construed accordingly.
(1A) Excepted from the definition of "broadcast" is any internet transmission unless it is--
(a) a transmission taking place simultaneously on the internet and by other means,
(b) a concurrent transmission of a live event, or
(c) a transmission of recorded moving images or sounds forming part of a programme service offered by the person responsible for making the transmission, being a service in which programmes are transmitted at scheduled times determined by that person.
So if you were, say, recording a series from a broadcast on Sky TV channel (other paid TV services are available) and then timeshifted it to watch after your Sky subscription ended you'd be ok, Netflix? Not so much.