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Hard to tell from the photos but it looks like the cement cill has been rendered and the extra height is obscuring some of the wood frame. I have seen this done in some places and it's a bitch from a carpentry point of view.
There are a number of materials you could use there but you will need to take care removing the existing or just bodge it and cover it.
One option would be Repaircare Dryseal you could probably use masking tape and go right over the whole lot just to get through to a proper fix. Or strip the dead stuff out and patch with dryseal, or take on the whole job properly and find out why that window frame is rendered in. Usually it's because the frame was rotten and some cowboy suggested rendering as an option.
A cheaper putty in a tube is Top Gun.
I've just put some Purlfrost up in the bay window, and I noticed while cleaning the window outside how fucked it is.
It seems as though there's very little holding the window in place.
What am I going to need to fix it? Is it a cement job or window putty?