How does this work exactly? Our 12 month contract ended and he basically offered 12 month again or leave. He did this ~2 weeks before the end of the contract so we didn't have much choice (never gonna find somewhere in 2 weeks) but now we're stuck here for another 12 months

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I hate renting.
If they are genuinely willing to tell you to leave then you have no choice. However, they have no good reason to do this. An existing tenant is in a very strong position.
Firstly they need to have given you appropriate
section 21 notice before the end of you fixed term. 2 weeks is not even close to enough.
If they haven't then it will automatically go into a rolling tenancy (periodic). They would then need to serve appropriate notice from which you will have to leave. If they wish to increase your rent as part of the switch to a periodic tenancy, they again need to serve you appropriate
section 13 notice. Until then the rent is the same. If you want to play ball, you can overlook the lack of notice if the increase is reasonable and just appease them, especially as I'm sure you expected an increase in rent.
If they have done everything correctly, you are willing to accept the increase in rent, and they are saying they would like you to sign a new fixed term or leave (as per their notice) then they are bluffing in my opinion. If they are simply annoyed at not getting the £50-£100 in renewal fees it is an even greater bluff as that is not an instruction from the landlord. The landlord will be annoyed at them, for costing them far more money over £50-100.
They would have to find a new tenant which will cost them in resources and the house will remain empty. Even if they would like someone tied in to a 12 months contract, they may as well wait until you leave rather than having to hunt for someone right now. There is no difference.
I'm renting at the moment in a property managed by a major letting agency for 2.5+ years now. They are probably taking 15% of the rent for doing nothing. When it comes to fees, they waive everything I ask them to. After all, they are getting 15% of the rent for doing very little. Their rent increases have been in line with inflation which has been very low recently.