I'm not quite sure what you mean by recording Freeview. Freeview is a steaming service, which the main channels (BBC and ITV) have agreed to support. Unless you have specialist recording gear you can't actually record it.
I have purchased BT HD recorder which can record two live TV programs at the same time. I have upgraded the HDD to an SSD which is far more responsive and physically even quieter. It has fast forward including 1minute jumps forward and 15sec backwards, so its easy to jump the adverts when playing back.
Eh? Sorry Prof but you are well wrong there.
Freeview is an over-air broadcast service that carries the five main channels and many others. Agreed some of those channels can be delivered by broadband (a.k.a. streaming) but most are through your aerial. All transmitters (of which there are nearly 1200 in the UK) carry PSB1 (BBC), PSB2 (independent main stations) and PSB3 which carries a mixture of BBC and independent stations in HD. Main stations (i.e not relays) also have Com 4, 5, and 6 carrying bucket loads of other stations but as with PSB they are ALL off air. Some main stations broadcast local TV stations on Com 7 such as Leeds TV, York TV, etc and all of them are on channel 7*. The coverage of channel 7 is very limited so there should be no mutual interference. [PSB is Public Service Broadcasting, Com n is Commercial.]
[*Confusion point 1: Com7 is a seventh transmitter on the relevant site, but Local TV is station 7 - see below.]
You are probably confused by the fact that smart TV's as well as receiving off-air can also collect stations that are fed by broadband - such as BBC iPlayer, ITXx, My5 etc. Some recorders are able to use broadband fed stations as well.
If you have a suitable recorder with a twin digital TV receiver inside them you can record two stations whilst you watch a third. Humax has always been a popular brand, but others by Panasonic and Manhattan are also very good. Some of them (notably Manhattan) can also record off broadband. All of them by default are able to record HD whether your TV has HD capability or not.
There can be some confusion with the use of the word 'channel.' In analogue days there were five TV channels, BBC1, BBC2, ITV, Channel 4 and Five. Each of these five used one signal carrier transmission or channel so there was never confusion as to what meant what.
With digital transmissions - which have one multiplex on each signal carrier channel - the programs are converted into digital data and multiplexed or computer mixed together allowing as many as eight or more programs to be available on a single signal carrier channel.
On a personal basis I refer to the signal being radiated by the transmitter site as a channel, and what I watch at home - such as BBC1/ITV2/More4 etc- as stations.
So to recap, all transmitter sites - main or relays - carry PSB1-3 which in total presents 20 stations, but in addition main stations carry Coms 4, 5, and 6 (and some Com 7) which in total will decode into around 80 or so stations. Also each of the six over-airMultiplexes (or muxes for short) have the capability to carry audio only stations - i.e. radio - which is another 24.