The answer is yes and no.
Yes, as you can use UK based services such as TVPlayer, TVCatch-up or FilmOn. The catch with them all is that you need a Chromecast or AirPlay to easily get to your TV and have a good UI.
The bigger catch is that the video quality is very very average, if not poor.
The only online service I know of that is really good for high quality live UK TV is a Swiss outfit called Zattoo. That will only work if you VPN or Smart DNS to Switzerland. Smart DNS isn't free, but it is cheap, and although Zattoo has a free service, the video quality is horrid.
The positive side is that all up it costs probably around £6 a month or so, and that will give you near HD quality streams for the BBC channels and ITV1 and SD quality for the rest. Most major free channels are there, the UI is so good I prefer it to satellite, you have a near full PVR for home recordings, and it will also have available for catch-up, every programme from every channel for 7 days (normal catch-up doesn't include every programme).
There are full reviews
here, just select UK from the Live TV section.
Oh, and for Sky, Now TV is great and not too expensive for the Movies and Entertainment packages, they include live and catch-up. Best bet is to get a now TV box.
Finally, that Smart DNS which is needed for Zattoo will also get you so many other free services from around the world (US, Australia, Ireland, Canada, NZ etc), plus every region of Netflix if you subscribe to Netflix as well that it is worth the £3 or cheaper per month.
You can do it. Just browse through that website I linked, everything there and more is available via a DNS service, and there is so much available it is mad.