If your TV is 'smart' (i.e. it's connected to the internet), you can use the 'catch-up' apps on it to view many programmes.
If your TV isn't 'smart', you can make it so by buying a suitable external device, such as a Now TV Smart Stick
https://www.argos.co.uk/product/1165669
However many of the catch-up services you can get through apps on a smart TV are also available via websites. There's not a single website though; you need to go to different sites, depending upon which channels the programmes yo want to watch were shown on. See the 'Watch on a computer' links here:
https://www.radioandtelly.co.uk/catchuptv.html
That link omits to mention UKTV Play though, which is the (relatively new) way to catch up on content from UKTV's free channels, Dave, Yesterday and Drama:
https://uktvplay.uktv.co.uk
The links above won't cover all channels though. Many channels don't provide 'catch-up' services.