Everyone who can get a Freeview signal will get BBC One, Two, Three, ITV and C4 in HD on a Youview box, because that Mux is broadcast on every single transmitter and relay. In this case there is no point in BT offering it over IPTV.
BT TV doesn't sell itself as a solution for people who have Terrestrial TV reception problems. It's a complementary service. Replicating Freeview on IPTV is wasteful capacity wise, and there would not be enough extra viewers taking up the service because of access to freeview channels over IPTV to cover the cost.
People who have terrestrial reception problems, and it is only a relatively small number of people now who can't get a terrestrial solution, do have an alternative. It's called Freesat. There is nothing stopping them using a separate Freesat box for the free channels, and a BT Youview box for additional paid channels.
Bearing in mind BT, BBC, ITV, Ch4 are all stakeholders in Youview then maybe a customer could email them and ask why the PSB HD channels are not available on Youview via multicast as they are on BT Vision. See what they say.
Customers pay the TV licence fee and pay for the BT TV on Youview service. Surely the BBC in particular would have a responsibility to respond to such a query?
... my terrestrial TV signal has been suffering interference from a new 4G mobile network and the adapter to stop this blocks all the HD channels.
Going back to your original point.
Why would the 4G filter block any of your Freeview reception? Did you receive any TV signal on UHF60? Are you using the correct type of filter (59 filter or 60 filter)?