Why wouldn't you want it to have a tuner? There are plenty of HDD recorders with 500GB or 1TB drives with HDMI output and optical out as that's pretty much the standard spec. Plenty will record freeview HD too and normally they have twin tuners so you can record two programs at once and depending on which muxes those recordings are using you may be able to watch a third channel at the same time though most people would just use the TV tuner. Check out the usual sites like Comet and Currys and do some research on any models which look about right. I've got the Philips HDT8520 which has had a number of issues but with the latest firmware update is now reasonable and available relatively cheaply because of its past reputation. I think the general opinion amongst people who have tried various is the Humax brand - either Fox T2 for HD broadcasts or PVR9300T for SD only although I believe the HDD is only 320GB on that.
Sony Xperia Z5 review: Hands-on with the phone which the Z3+ should have been