By way of explanation, let's go back to the good old days when you had an analogue TV with a VCR. Both devices had had an analogue TV tuner built into them. So you could record one channel while watching another. (i.e. you need TWO tuners, not one).
If you could get a recording device (PVR, DVD recoprder, or whatever) without a Freeview tuner built into it [which I doubt anyway], you'll only have one tuner (in your TV set), so you'll only be able to record the channel which you're watching. Further, if you want to record something while you're out you'll have to leave the TV switched on (otherwise you'll have switched the tuner off).
That previous paragraph assumes that your TV set is actually capable of sending the signal from its tuner to an external device. (Not all TVs do that). If it can't, you wouldn't be able to record anything using a recording device without its own tuner.
Buy a 'normal' recording device (with its own tuner built in). If the signal strength isn't god enough for it to tune signals properly, try a cheap signal booster or look into getting your aerial system upgraded.
Chris