Yes, probably, mostly. But unless the DVR comes with a gadget to remote control the Sky or UPC boxes, you'll need to set the timer on both the recorder and the decoder box. Also you're taking MPEG broadcasts and re-ecoding them to MPEG again, this degrades the quality.
For best results and ease of use, go with UPC's DVR if you're a Chorus/UPC customer and/or Sky+ if you're a Sky customer. These record the digital stream perfectly and playback is identical to live.
The main advantage of an 3rd party DVR would be that you could make discs for playback elsewhere, but expect to find that some broadcasts (especially Sky) will have 'no-recording' flags sent and you won't be able to record them.