The following is based on my experience advising institutional investors - hope it's helpful! But don't make decisions based solely on this. Better to get properly informed and tailored advice.

You're asking how much risk to take in your runway portfolio. Currently you're taking no risk.

It makes sense to take risk if your investment horizon is long enough. Retirement savings are very long-term, so they can afford to be invested in risky, growth-seeking assets like shares. 

To give my intuition on the numbers, if your runway is intended to be mostly spent in the next 6 months, a bank account is a good option. If you have a more than a year or two to invest, it would be typical to start taking some risk in the portfolio, e.g. with a share allocation. Not with 100% of your portfolio, but maybe 20% or 30%. If investing for longer than 10 years, you could put 70% or more in risky growth-seeking assets.

The above assumes your existing retirement savings are off limits if you run out of runway cash. There is also an implicit assumption about your risk aversion. On that matter, your risk aversion should be applied to the aggregate of all your assets, including your startup itself which is a significant source of uncertainty.

The following is not financial advice. 

Sam Bowman who's EA adjacent has written about this. 

Wise actually has a bank account that you can invest in an index for UK customers only w/ 0.5% fees.

Note that investing in the stock market is generally seen as riskier than holding a major country's currency.

Also inflation is unusually high and markets expect it to come down and currencies are unusually volatile currently:

"Rock-bottom inflation and interest rates over the past decade helped smother swings in exchange rates. Deutsche Bank’s cvix index, a gauge of forex volatility, has been above its current level more than 90% of the time over the past 20 years. By contrast, the vix, which measures expected volatility for America’s s&p 500 index of stocks and is often used as a measure of overall market sentiment, has so far spent October at roughly its long-term average." [src]

If you want to take as little risk as possible, you're right that cash is not the safest investment because it's vulnerable to inflation. It would be safer on a real basis to invest in something like Harry Browne's Permanent Portfolio, which is 25% cash, 25% stocks, 25% Treasury bonds, 25% gold. Just make sure your investments are liquid enough that you can sell them quickly if you need to.

If you are under 40 and might want to spend the money on a first property costing <450k, you could consider a Lifetime ISA (either cash or stocks & shares):

https://www.gov.uk/lifetime-isa https://www.moneysavingexpert.com/savings/lifetime-isas/

You might find this article helpful: https://80000hours.org/2015/10/common-investing-mistakes-in-the-effective-altruism-community/

Not financial advice. It's hard to give a specific recommendation since it depends on details of your personal situation and how risk averse you are. As a general rule, if your runway falling by 20% would still leave you with adequate runway (as defined by you), then investing it would likely be best for your long term wealth.

As you suggest, an index fund would be a very sensible, lower variance option.