"so it would fit six new HD TV channels"
56 MHz / 8MHz = 7
That's not 7 HDTV channels. That's potentially 7 x DVB-T2 Multiplexes.
If you used robust coding and DVB-T2 (all UK Freeview HD boxes get DVB-T2 and older DVB-T boxes and TVs won't receive MPEG4 / HD anyway) then you have maybe 25Mbps, allowing about 3 or 4 statistically muxed HDTV channels. It's likely possible to do 6 HDTV channels on one DVB-T2 mux with less robust coding.
But for a Nationwide Network you can't use all 7 mux everywhere, as a SFN will likely not work nationally.
So maybe between 2 and 3 Mux Nationally, maybe SFN in some areas and thus between 6 channels and 18 channels Nationally. Depending on Coverage and Quality.
If you leave out areas with co-channel interference (satellite?) maybe you could have 4 Mux nationally and 80% coverage with 20+ HDTV channels.
TV3 in Ireland only had about 80% coverage on Analogue. Five coverage on Analogue wasn't great which is why they were on Analogue Satellite before Sky Digital Launched.
Any commercial deployment will care about most channels for least Multiplexes and 75% to 80% coverage if allowed as 99% coverage nearly triples the cost for <18% more advertising revenue as likely rural people have satellite, and only existing Satellite or Cable channels might consider this expensive addition.
Really actually it's not economically viable.