Let me start by saying I am implacably opposed to student debt. My political/moral position is that HE should be paid for via income tax.
However, leaving that aside, it's probably not good to think of the debt as 'personal debt' but more like a graduate tax. Your DD will be paying the student and tuition fee loans slowly, over time, as she earns. It's not like meeting loan payments that must be met come hell of high water, whether you are earning or not, e.g. a mortgage.
Secondly, the value of money has changed dramatically. You may have bought your house for £60k, but you also say that was before she was born - so over 18 years ago!! Back in the days when Mars Bars cost about 20p!! And how much is it worth now/how much is a Mars Bar now? Do bear that in mind.
Thirdly, the difference between a graduate and non-graduate salary is growing. Over a lifetime, it's now averaging £500,000. Puts the £60k into some perspective, doesn't it? (Yes, yes, I know that there are loads of people who have graduated and aren't earning much, and loads of people who never got a degree who are doing really well, but this is an average, right?)
Fourthly, she can and will need to get a job to get herself through. You shouldn't remortgage your own house to help her - don't even think about it, because that's your financial security gone. Lots of students have to do this, and it doesn't necessarily impact negatively on their grades unless they have a very hours-intensive course. Even a bar job, if stuck at, looks impressive on a CV. Shows the student has some grit and some sense of the value of cash.
Fifthly, as others have said, you urgently need to do some research because there are vast differences between, say, the cost of studying in London and the cost of studying in Leicester. There are also vast differences between the salaries of some graduate jobs compared to others. Whether the risk is worth it really depends on what she is doing and where.
Sixth, do a budget! Work out what she needs for rent, food, course books, etc and how much she needs to earn to make up the shortfall.