Best way to fill a crack in a table

[Diver Fred]

That's way out of my skill base.

Prob not going to help but Mrs wants the table Infront of a radiator

In that case I'd try using these
https://www.screwfix.com/p/stretche...8-x-28-x-25mm-10-pack/12920?_requestid=182321

Only fix using one screw in the slots in the direction the wood will move. I'm sure you can work out which slot to use.
A pack of ten should be sufficient to fix that table top

 

[big-all]

be prepaired for it to keep moving and the filler cracking and falling out
now nothing may happen or it may carry on moving you can never tell but mending plates every say every 150-200mm may help or a bit off 2x1" par[21x43mm] screwed along the gap
https://www.toolstation.com/mending-plate/p52354?searchstr=mending plates