If you really have your heart set on replacing the lock sets on those, I'd recommend taking the whole door off with the handle and hinge included and taking it to an architectural recycler.
As noted in a comment, these appear to be made of wide solid boards and those handle/lock sets are old and a lot of people actually like the old look. As a complete set of door and handle, they'll be worth a fair bit of money. It's hard to tell from the two small pictures, but they seem to be in pretty good shape and may well get resold with almost zero work from the recycler, so you should be able to get a fair bit of money out of them.
Once you've sold them (or at least ensured that you'll be able to sell them), go to your local big-box store and buy some cheap luan interior doors and bland, modern knob/lever sets and replace the doors. If things go well, you'll almost break even on the project, price wise.
I'd suggest calling a couple of places and asking them how they'd go about giving you an estimate on what they'll pay you for the door/lock sets. They may send someone to you to look at them and offer you cash on the spot (not so handy if they're taking the bathroom door!), or they may ask you to bring a door in so they can give you an estimate. If you need to bring one in, it should be quite simple to pull the hinge pins and put the whole door in the back of a SUV, minivan or pickup truck. (Ah! You're in the UK. You could probably easily strap it to the roof rack of a small car, or I've seen many with trailer hitches - put the door in a trailer, even if you have to hire one for the afternoon.) Just be sure to wrap it in a blanket or two to prevent damage during transport.
There's a good chance that you'll get more per door if you sell them a full set of 9 doors, than if you sell one at a time, so be sure to discuss that with them, and be prepared to live without doors in your house for a few days as you work to install the new ones.
To address the new issues in the edit:
Lock the doors
I'd suggest either a locksmith (after all, that's kinda their reason for being) or again, take a trip to an architectural recycler - they may have keys that would work with your doors.
To lock them from the inside without the key, you could install a barrel lock, though, IMHO, that would look pretty poor.
This is the type of latch I'm referring to:
image courtesy of lowes.com. No endorsement intended or implied
This one is, at least, black to match the rest of the door hardware. Again, I agree that it wouldn't look all that great, but it would at least match color wise.
Also, you could hang the key on the knob by a string on the inside, then at least, you'd always know where it is when you need to lock it. I presume you're most interested in locking bathroom doors to avoid uncomfortable interruptions, so that would work. You could put up an extra towel hook to hang it from so it doesn't bang against the door every time it's opened or closed.
On door hardware like that, there's a good possibility that the handles are affixed to the turning shaft by set screws. It might be as simple as loosing the set screw, pushing the knob back on, and tightening the set screw.
I'd suggest a whole new question focused on that only, with detailed pictures of the knobs if you're interested in figuring out how to repair them.
Doors look old
Some people like that, some people don't. That's a matter of opinion and design and is explicitly off-topic for this forum. If you don't like the "old" look, then by all means replace the doors! Just don't scrap them - doing so is throwing away money.
You can, to an extent, fix up the scratches and dents and multiple coats of paint. Strip the paint (using a paint stripping chemical, not a sander - there could be lead paint in there and you don't want to breathe the dust, plus liquid strippers are much better at getting paint out of details without destroying them), fix up the bare wood (stop by the woodworking sister site with detailed pics of the damage to ask how), then either stain if it's nice wood or repaint if it isn't.