Welcome Elh,
You're doing incredibly well for 24.
As you are paying 40% tax , you could consider putting the money that you are paying the higher rate of tax on into a personal pension. The upside of this is that you will delay paying tax on it, and will probably pay less tax in retirement, and you will get to take advantage of the larger tax break before it is taken away (which may or may not happen). The downside is that you wouldn't have access to it for at least 30 years and likely more.
Are you thinking about retiring early?
You will still be covering your expenses when your income decreases, so I'm assuming that you are trying to save as much as you can now for FIRE, rather than save now to consume more when your income drops.
In terms of expenses:
Have you checked that a travel card is still cheaper than PAYG as you WFH one day a week? What about shorter weeks? Have you looked into getting a Santander 123 credit card to get some cashback from this? Could you cycle to reduce travel expenses? Are you under SDC (Supervision, Direction or Control) meaning that you can't claim tax back on travel expenses?
Have you looked into claiming your £4 tax per week for using your home office? (Assuming you are required to WFH).
Any annual costs you need to add a monthly contribution for (TV licence?, phone upgrade, home appliances?)
Lunches and takeaways you've identified as an area to save.
In terms of what to do with surplus cash:
Efund is high - you're not going to reduce this [or invest it?] => fine. Consider moving it to a higher interest current account (outside of an ISA) as you still won't pay tax on the first £500 interest, and can move nearly all of it all back into a cash ISA at the end of the tax year if you want.
As soon as you can contribute more to the workplace pension I'd do it - you'll save on tax, NI and get a match from the company.
I personally would put all the extra cash into Vanguard (in an S&S ISA) rather than the mortgage, because I'd expect it to grow more than 3% per year on average. This is a personal risk tolerance thing, and it seems like it might feel too risky for you at the moment. At 24, without dependants, without a major purchase on the horizon (that you've mentioned); many people would say you can afford to take risk and invest at higher volatility (more stocks) for the long term. If you don't feel this is right for you then it probably isn't - maybe read Tim Hale's Smarter Investing for some more information, and check out the risk profiling company he recommends, (but google it to do it for free).
If you don't want to invest more, maybe look at opening regular savers at other banks, HSBC and First Direct both have 6%; and there are more 4% and 5% ones. Even after tax, getting 6% is better than saving 3% on a mortgage.
Plenty of people here have paid off their mortgages first, and there are pages of debate as to whether it is 'better' or not; but it is a mathematical certainty that if you borrow money somewhere at a lower interest and earn a higher interest/growth (after tax and expenses) you will make money.
How does your mortgage work in terms of borrowing back the overpayments? If you can't borrow them back whenever you like (as you could for an offset mortgage), then overpaying the mortgage may give you less security than you think (until it is fully paid off). Your choice and not going to force my opinion on you.
For your boyfriend moving in:
Have you discussed all the joint expenses and how you will split groceries etc?
Have you discussed whether you think he should have an interest in the house if you separated and compared this to the law?
Have you told your mortgage provider? (they may require him to sign a form saying he doesn't have an interest in your property), and not telling them may be against the T&Cs of the mortgage.
In Summary:
Good work so far.
Consider a personal pension to pay less tax this year
Look for high interest accounts as an alternative to your E-fund ISA and/or mortgage overpayments
Look to invest more (by learning more) as soon as you are comfortable with it.
Maybe change the title of the case study to include 'in London' or 'in UK' to get more local comments?