She doesn't want to grow old living alone and she wants us to help with her care when she is older and dp is fine with this.
Of course he's fine with that! It won't be him doing the caring!
I completely understand the MIL's position, and she is wise to protect her assets, but it would put you in a very precarious position.
Some people are saying you have nothing to lose, but they're missing the point that when you split up (I do believe it would be "when" rather than "if", and so does your partner it seems) you will have the hassle of trying to find somewhere to live, and will have to find many hundreds of £ to pay deposit, fees and 1st month's rent, plus other costs, such as buying furniture, van hire, etc.
If you will have to rely on housing benefit, you will have difficulty finding a landlord who will rent to you. As such, when you eventually find somewhere, it will be a grotty place, in a horrible area. I know you said the new house will be nicer than you have now, but is the place that you're living in as bad as what I've described? And wouldn't it be better to just stay where you are to avoid all that?
I also believe that it's not just your MIL who doesn't want you on the deeds. You said he's complained about his ex getting half his previous house, so he's going to make sure he doesn't put himself in that position again. But he looks more reasonable if he makes out that it's because MIL doesn't want it.
Really OP, this has a big red warning sign flashing above it. You would be a fool to agree to go along with it. Although as a pp mentioned up thread, I'm not sure if it would even get off the ground, with regards to getting a mortgage, due to your MIL's age, unless they pretend that she's gifted the deposit. However, as she would have to sign a declaration stating that it's a gift, she would not be protecting her assets, so there's a bit of a contradiction there.
So, in summary, don't do it.