Consumer information, not legal advice. Anything specific to your situation belongs with a qualified solicitor. Rules shift, so check current guidance at Ofcom and gov.uk.
The 30-second answer
Yes, IPTV is legal in the UK. It is a delivery method, sitting in the same category as Freeview, satellite or any streaming app. What decides legality is narrower: whether the particular operator sending you those channels paid the rights-holders for them. Lawful technology, occasionally unlawful use of it. The IPTV Wikipedia entry is a reasonable technical primer if you want to understand the mechanism itself.
What IPTV actually is
Internet Protocol Television moves live channels and on-demand video across an ordinary broadband connection using the same protocols as everything else you stream. Sky, BT, Virgin and Now all run IPTV-adjacent delivery inside their own platforms. So does iPlayer. So does Netflix. The mechanism carries no legal weight of its own and is lawful everywhere it exists.
The three categories: and which one your provider sits in
Every UK IPTV service sits in one of three buckets. Working out which bucket yours is in tells you provider is what this whole question really comes down to.