Partly depends on what exactly you mean by the words 'we have a joint income that allows us to live comfortably, as long as we budget super tightly, and there is nothing left over' and your definitions of 'comfortably' and 'super tight budget', but you seem to be suggesting that you have a lump some somehow leftover from a house purchase? Did you buy a cheaper house than the one you sold?
You could always pay back some of it onto your mortgage if you have one and are allowed to make overpayments (most allow 10% of capital each year as an overpayment, but check the terms).
An emergency fund is always useful, especially if you would struggle to pay for significant house or car repairs, major works such as a new roof, windows or bathroom, or car replacement, so you could always save it and use it for those sorts of things.
If you are saving it, you need to get the best interest rate possible, this will be in current accounts, which can be a bit fiddly to meet the pay ins and sometime direct debit requirements (they don't really want you to use them as savings accounts).
An easy way, as long as you are disciplined enough not to spend all the money because it is in your current account would be to make Santander 123 your main current account, and you will get 1.5% interest on up to £20k and cashback on your bills which should exceed the £5 monthly fee (we get about £4.50 pm and our bills are lower than average (band A council tax, total of £20 pm on phone contracts, no pay TV).
If you haven't already reviewed your budget, you could go back to basics and go through the Moneysavingexpert budget planner to get the best price on all your bills, think about reducing unnecessary expenses such as insurance policies you don't really need and get the best interest on your savings as well as thinking about whether you should overpay your mortgage with some of the £15k.