There are two important questions here:
- How much money should you leave yourself for emergencies?
- What is the best use for your extra money?
Many people in the US suggest ~6 months worth of expenses as an emergency fund, but you need to pick an amount that you are comfortable with. Don't exhaust so much of your savings paying off debt that you are left with some anxiety about an emergency.
Separately you need to decide the best use for your extra money, what can you do with it that will best help meet your financial/other goals. If getting out of debt is the goal, then you just need to calculate the net impact of each £1 of debt repaid.
In simple situations you just have to compare the interest rates and pay the higher rate debt first, all else being equal that is always the most efficient way to repay debt. Things that can complicate that math are adjustable/variable interest rates, tax differences between debt types, early repayment penalties. You'll want to do your best to calculate the effective interest rate you are paying on each type of debt by factoring in tax differences and early repayment penalties. Adjustable rates are trickier, but you could calculate based on some projections.
If your rates are fixed at 3.25% for the student loans and 4.29% for the mortgage, and there's no tax benefit for either kind of debt (or equal benefit for both kinds of debt), and there's no penalty for paying either off early then you should put extra money toward the mortgage. If your rate isn't fixed on the mortgage for the long-term, then you are faced with estimating how much it might change in the future, but it seems unlikely that they would go below the rate on your student loans before you have those paid off, so likely the best option is to pay extra towards your mortgage.
You also want to factor in safe returns, for example the last time I bought a used car they were offering something like 1 or 2% financing, while CD rates were over 3%, it made more sense to use my cash to open a 5-year CD than to buy the car with cash. This is the opportunity cost of paying off debt early. Some people will use average market returns to justify not paying off any debt early, but I suggest sticking with safe return rates since market returns fluctuate and complicate things in the same way as adjustable/variable interest rates on debt.
There are other things that could be factored in, like the value of accessibility (home equity can be tapped easily, while other new lines of credit might not be), or potential changes to tax law, and probably a dozen others, but adding too many unknowns and predicting the likelihood of each will overcomplicate things very quickly.