The idea of having a buffer for emergencies that you never had before, seems sensible. The concept of it being an emergency buffer is of course that you hopefully never need it, but when the emergency comes along you would be glad you had it. As such, you can't really invest it in something that has the risk of going down in value unless you are going to commit more to your emergency fund than you think you could ever need.

If you "invest" it in this low interest environment there are no easy options that guarantee real terms growth; even trying to make enough investing gains to break even in real terms carries the risk that the assets decline in value instead of going up. So, that leaves cash deposits, high interest current accounts and regular savers etc. Maybe premium bonds if (s)he's a high rate taxpayer who already burns through their personal savings allowance -PBs pay on average a bit more than ISAs albeit the interest rate is a gamble.

As leaving cash on deposit at low rates feels like you are not getting much out of it (although of course what you're getting out of it is a safety net in case of disasters and emergencies), you / partner should make sure you are realistic about how much should be needed in the pot, and not be unnecessarily over-the-top supercautious.

Remember the total funding available in an emergency, crisis or other time of need is what you have in cash, what you can access temporarily on credit (without massive cost), what you can bear to liquidate from an investment portfolio (which might be standing at a loss) what support you can get from a partner's income (depending on strength of the relationship at that time), what you are willing to beg or borrow from friends and family etc.

So, she should assess what sort of emergencies she's trying to mitigate, put a large part of those emergency needs into cash or near-cash accounts at the best rates you can get, and then look at the world of investments for the rest. Depending on age and income the investments piece could involve pension as well as s&s ISA, but what funds you buy within that investments piece depends on attitude to risk - e.g. medium risk, low to medium risk etc. If preference is for low or very-low risk investments, probably "all in cash" is an ok solution.

Your emergency fund should usually cover 6-12 months of your regular spending and any other 'one-off' spending you have coming up over the next couple of years. This money should be in cash and easily accessed.
This is Money website has a good summary of best buy tables for cash savings: http://www.thisismoney.co.uk/money/article-1583859/Best-savings-rates-General-savings-Internet-branch.html

If after working out how much you need in your emergency account you have funds left over then you may want to consider investing the money. First you will need to consider what you are investing for and ensure the timeframe is long term (ideally 20yrs+).

....and of course there is an equivalent closer to home, linked from further up this page:

https://www.moneysavingexpert.com/savings/savings-accounts-best-interest