Is £10k emergency fund enough? If you feel your job is very secure, then around 3 months of monthly expenses is sufficient. If you feel your job is not very secure then I would do 6 months of monthly expenses. £10k may be right for you or might not... so firstly I would review that.
Any debts other than the mortgage? If so then I would pay those off over the next year as the priority.
Company pension - is it a defined contribution scheme (auto-enrolment) or a defined benefit scheme? Defined benefit schemes are not that common now, so for the following I will assume it is a defined contribution scheme.
With a defined contribution scheme the money you pay in is yours, even if you leave the company. The pension follows you, future employers can contribute to it, or may have different scheme so you end up with several.
You say the company pays in 3%. If you are paying in nothing and the company are paying in 3% regardless, then that's a start. You should look at making contributions yourself - your company may be doing a salary sacrifice scheme which takes contributions you make directly from your pay, this can be worth doing but do read about it carefully as salary sacrifice can affect other things as it lowers you pay.
As a higher rate tax payer it is worth you paying into your pension, as you can claim 40% tax relief on all that you put in. Your pension scheme provider will claim 20% automatically, you will need to complete a tax return to claim the remaining 20%.
I would read as much as you can about how pensions work and also about other tax efficient savings such as Stocks&Shares ISA. You can contribute up to £40,000 a year (or max of your income if lower, which in your case the £40k is the lower figure) to your pension and up to £20,000 to an ISA.
Useful resources:
Meaningful Money Podcast... currently at the end of a series about pensions, so start with the first in that series: meaningfulmoney.tv/2018/08/08/what-is-a-pension-pensions-masterclass-1/
Pete the financial planner who does the podcast has also got a book out, which you may fancy having your Christmas Book list. The third section of the book is about investing which will give you a starting point for getting to know your risk tolerance and about stocks vs funds.
The Meaningful Money Handbook - www.petesbook.com
Money To The Masses Podcast - another podcast that is useful to listen to.
Pension calculator: calculators.moneytothemasses.com/pension
Article about how much to pay into a pension: moneytothemasses.com/saving-for-your-future/pensions/how-much-should-i-pay-into-a-pension-each-month
Pensions Advisory Service - has articles about pensions, for example this one about salary sacrifice: www.pensionsadvisoryservice.org.uk/about-pensions/saving-into-a-pension/salary-sacrifice
Starting young is great... you have many years ahead of you for investments to grow. Well done for getting this far, wish I had been in your position when I was 25.