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Is there any way I can still use my old Sky box to record (its an HD+ one) or will that function become unavailable?
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No. Part of your subscription is to use the recording features. Once you stop subscribing, you're not allowed to record, or VIEW YOUR RECORDINGS, on the box. You CAN keep paying them the ~£10 per month fee to keep it, but this is exactly what you're trying to get away from.
If you want to directly replace the Sky box, yes, you get a Freesat recorder. If you want the on-demand features, they call it Freetime.
If you have an aerial and want to use that instead, you could buy a Freeview recorder, or, again, to add on demand (and a very nice interface), Youview.
In either case, Now TV should be considered as 'Sky on demand' and either of the above devices will do the on demand job better, with the exception of all that lovely Sky content. Just so you're aware, loads of devices can do Now TV, you don't specifically need the box - PS3, Xbox for example. Maybe your Smart TV even has NowTV.