That because the band is miming to a "live" recording they made earlier - it might look and sound live, but it just wouldn't work in TV - they always record the musical sound separately and just have a vocal mic on to give the illusion.
Not true! At least, not always...
I notice you're from the UK. This might explain something. For some reason, in the UK, Canada, and Europe (as well as Japan and S. Korea)- it
is standard procedure to perform "full-playback" or "playback w/ live vocal" on televised shows. For example, I've appeared on 'Top Of The Pops' where indeed I was playing along to the recording. Jules Holland, on the other hand, you actually
do play live!
Here in The States', however, "full-playback" is the
exception to the rule. Yes, sometimes, an act will "fake it", but most actually play live. I've done most of the big shows on U.S. tv (Letterman, Leno, Ellen, Conan, Good Morning America, etc...) and we have always performed live- no playback or pre-recording!
Some of the shows (Conan O'Brien's former show, for instance) do allow you to go in and punch-in any 'fixes' after the taping. I never have, but the option is there.
I'm not sure why the trend is different in other countries, but the pattern definitely exists! I'll be performing on the Canadian CMA Awards in a couple of weeks. Full Playback.

And the band is really good! Oh well... that's how they do it every year.