I want to summarise your question slightly differently than written.
- You have a house and like your own space.
- Your friend has been given 6 months notice to leave his place, is struggling to find a new place, and wants to "move in" (not the same as staying temporarily); you think he may be taking advantage of the situation.
- You have told him he can move in for up to 2 weeks, with no rent, but you don't really want him to stay longer; however you fudged saying "no" and your approach has probably implied to him, an understanding that there is scope to stay longer (on some or other terms).
You have a real problem here. Your friend has 6 months to look, but why would he, when he can use some of that time to see if his good friend with a 3 bedroom house will let him stay. After all, you've virtually said something can be agreed, haven't you? Or that's how he may well feel. And, if not, you're hardly going to throw him out on the streets, homeless. Not with a friend homeless and some wishy-washy "Wahh, I like my spaaaace" excuse - and not when you have 2 spare bedrooms and him already there. Do you really have what it takes to kick him out on the streets? What if he genuinely cant find somewhere? Homelessness? He may well reckon, "probably not", and that you'll reluctantly decide you're okay with it. He's probably right, too.
So its a win for him every way.
What to do? I think the only thing you can do is a "frame reset" - sit down with him in person or voice, and start over again from scratch.
"I know what we discussed, and I impulsively said yes. But I've been thinking since, and it's not going to work, and we will both get hurt worse if we try it. I'm sorry, but I'm changing my answer to 'no', and I want to explain why."
Notice it's not vague, and not open to ambiguity. Its very direct; it's a statement of how things are, and not the prelude to a re-negotiation. That's deliberate. That also makes it the hardest thing to say, but you'll need to be that direct and honest.
That's how to start. After that, is down to you, so I can only give ideas..... some or any of these may help.
I didn't get this house at random. I got it because I need space, and a place totally to myself, badly, for my own wellbeing. I realised I can't have someone staying longer term in it. I wouldn't be able to manage well, myself. That's my mental wellbeing, and my personal lifestyle, so its not a matter of compromise, its just how it is. I won't be sharing my space long term. I kind of fudged the point initially so I need to be clearer now.
I'm also reluctant because of the contradiction in your own request.
You have 6 months notice. It's a long time. If you can find somewhere else within 6 months, you won't need my help anyway. But if you honestly can't find somewhere else in 6 months, what does that imply about the chances you'll only stay 2 weeks after that? If you sincerely look for 6 months, and fail, the odds have to be that you might not find anywhere for another few months. Or more. A year or 2.
So your own question says to me, there is almost no scenario where you stay here and only need to stay a couple of weeks. If you stay, its because you failed to find somewhere after 6 months, meaning it's that hard to find somewhere, and you'll need to stay semi permanently. Isn't that true? (get his agreement, yeah, that's probably how it would go).
If we do that, we're both fucked, I'll want to evict you for my own wellbeing, you'll have nowhere to go, we get stuck into lawyers... I value our friendship enough that I'm not going to go that route. A situation we can't easily put right.
You have 6 months till you actually have a problem. If you can't find a home in that time, you've got a problem that I can't help fix.
But ..... if you find somewhere, actually sign a binding contract, and there's a week or 2's gap, and you need a helping hand over the temporary gap, yeah. I think I could do that, and love to help. No rent, no moving in, but couch-stayover for a week or 2, that kind of thing I can help with.
(Note - if you do let anyone stay temporarily for a while, look up "licence to occupy" - that's the legal term for when you let someone stay but they don't get any rights to stay against your wishes, like a sitting tenant might. There are forms and templates online for these as well, which may help.)
Source: personal experience of closest friend taking a friend as a "temporary" housemate and being driven to despair when it quickly became obvious temporary meant semi permanent in reality. Following that, I gave the same advice as I've written here, to 2 other friends considering "helping out a friend" with a room, and in each case the outcome was along the lines of "thanks, I didn't know how to say no, and I didn't see the problem down the line". That first case, the friendship was destroyed by the incident. The other 2 it survived. But how to.say it is as important as what to say - to know how to.set boundaries and draw lines. I've learned that as part of an open lifestyle where boundaries and communication are critical, and use the styles described almost daily as needed, they work very well.