As you both earn well, you could be in a much stronger financial position in just a couple of years. Have you seen the financial flow chart? It is an excellent decision making flow chart that will help you: The UK Personal Finance Flowchart - UKPersonalFinance Wiki
You have a lot of mortgage right now, with a very long term which means you will be paying it off in your 70's which isn't ideal. I know this isn't unusual in some areas of the country, but it's not a position I would like to be in. You also have a lot of equity in your house. You run the risk that mortgage rates will go up too, and that will eat into your spare income. Personally, I'd be considering downsizing or moving to a cheaper area and make more of my wealth more easily available.
The trust that you will get in 10-15 years won't pay half the current mortgage debt, so you can't rely on that to clear your mortgage.
Do you have life insurance to pay off your mortgage in the event one or both of you dies? If not, I would suggest this is essential to do immediately.
So, onto the short medium and long term financial stability.... we have cash savings of a year's income. I don't earn much and if my OH loses his job he's going to struggle to find a job in his field at his age. You can get by with 6 month's worth of cash if you have a death in service benefit with work, and also a good sick pay package (OH gets 6 months on full pay). After 5 years in this job, he is finally feeling we could reduce our cash buffer to 6 months of expenses instead of 12.
If you spend this cash buffer on new car, washing machine, essential house maintenance etc) then you have enough disposable income to top it back up quickly.
For the long term, you need a pension - do both of you have workplace pensions? Is either of you a higher rate tax payer? If you are, then after building your 6 months cash, I would put any income that attracts 40% tax into the pension, salary sacrifice is best but you'll get that 40% back either way from the government, so it's the quickest way to see your money grow!
If not paying 40%, then you need something for the medium term, a S&S ISA - you are right to be worried that if you need money in a hurry you don't want to have to pull money out of S&S investments at a time outside of your control. But if you have a 6 month cash buffer, you have a 6 month window to withdraw your investments. You should also build up your ISA with monthly contributions - the money you put in now will have longer to grow. Ideally you want to leave it for 5 years so that if there are any dips in the market, there is time for it to recover. Hopefully you've got 5 years before you need to use any of it.
Good luck!