Some great suggestions here and food for thought for you, OP, depending on what you want to prioritise.
My thoughts are (or what I would do if I woke up in your shoes with this issue) is to allocate the £65K into an account or pots. I think you feel unsure at the moment as it is just a big pile of ‘unlabelled money’ at the moment, making you feel twitchy, whereas if you have it allocated, it would help focus your thinking.
So, immediately, separate off an amount equal to 3-6 months of your net income. As you are a single parent, with the responsibility of a daughter and a mortgage, I would go for the full 6 months.
Next, separate off the amount you want to pay off your mortgage. If the amount you have decided is £20K, then fine. But I would spend a bit more time researching this, as paying down/off your mortgage quickly is great for security (especially as a single parent), lowers your monthly expenses overall (so perhaps you could reduce your hours or take say 3 weeks unpaid leave a year in extra holidays), and it means you could have less in the bank as an Emergency Fund.
Next, I would start a Self Care Fund and a holiday fund, with the aim that these are not for saving, but to be spent. The self care is on things to make your life easier, buy back time for you and therefore make the time you do have with your daughter better. This might be labour saving things - a cleaner, a dishwasher if you don’t have one - or things that give you back your sparkle - massage for tired muscles, more frequent hairdresser appt etc. As you already have holidays you are happy with, the holiday fund is more for weekly/fortnightly adventures. Depending on the age of your daughter, maybe Friday nights are cinema and meal out nights with Mum, or Saturday mornings are brunch or morning tea/high tea somewhere, or trips to zoos etc. Just an activity every week or fortnight that is special and will give you both lovely memories. Soon she’ll want to be with her friends all the time and these will be lovely memories to look back on.
Finally I would start a fund for my daughter for either university or house deposit. No need to decide which now, but knowing you have the money to help her in future if needed will be nice. But I would keep it under your own name for now, as something may happen to you and you need it to secure your own future, or alternatively circumstances may mean you may not want your daughter to have access to such a sum of money in maturity! So keep your options open.
If it were me, I would give that set up a go for 12 months (or up to when your rate expires and you are paying more of the mortgage) and then reassess how I feel and my priorities then.