Repairing rot in sill under sliding doors

[SouthLondonCharlie]

I have sliding French doors with an external timber sill that was damp at one end last year due to surface varnish having worn away. I repaired with filler & repainted with gloss. However, rot seems to have got in and the internal sill is rotten. Is it possible damp is coming up from the ground or is this old damage? I'm not sure how to repair - would it mean removing the doors and get all the rot out and make good? thanks.