There are 'watch live' options in the catch-up services for BBC, ITV, Ch4 and Ch5. Dontbforget, each service offers a number of individual channels, so theres quite a lot of coverage.
For other channels, their streaming services vary.
Hypothetically then, this seems okay. I think BBC iPlayer works pretty well. I'm less enamoured of the commercial channels. I think they see it as an opportunity to fling a load of adverts at the viewer before they're allowed to watch anything. It's definitely not the same experience as channel surfing live broadcast.
I've looked at more than a few Web services thatnpromise coverage of live TV, but unless its a subscription service then they run into rights issues repeating the UK live channels. I found plenty of stuff from foreign broadcasters who don't run such a tight ship on licencing.
There is talk of Freeview starting to migrate all its channels to online. This won't happen in time for your move, but it is the longer-term plan.
Sky also wants to divest itself of satellite broadcasting and go entirely to streamed services. When it does, that will affect Freesat. The earliest date that Sky can close its satellite operations 2030 when the licence to use the Astra satellite is up for renewal.
Since you're going to have to pay for a TV licence to watch iPlayer, I would have an aerial or a dish put up and use Freeview/Freesat until the dust settles on getting better streaming running.