First time back in Europe in over 30 years

You can use any leftover currency to partially pay your hotel bill and credit card for the rest.
You can use leftover currency to buy snacks or souvenirs at the airport.

of course you can "convert" them, you just buy the local currency with your GBP when you get there. You'll see currency exchange at each airport and all over major cities. Oh it won't be cheap and likely at a terribly disadvantageous exchange rate, but it can be done. Or you can just keep the GBP and sell to another traveler when you get home.

If your Capital One 360 is a credit card, you'd probably do best not to use it to get cash. A real ATM card is preferred for that purpose.
Otherwise, use your credit card every chance you get instead of using cash--meals, etc. Many transit companies dispense tickets through vending machines that also take credit cards. Just make sure you have a 4 digit security code on any card.
You can certainly convert the pounds into other currencies, but it'll cost you dearly. Why don't you just save them for your next trip?
The British Museum in London is really something--and it's free.

What Mary said.

You may well be able to get away without withdrawing any cash at all for such a short stay and put it all on your card(s).

Coins are not typically accepted at currency exchanges in other countries, so focus on spending the bigger coins in Britain (and the same plan later for Swedish Krona), even if you will change the bills elsewhere.

There is no current way in Europe to deposit bills into an ATM unless you have an account at the bank running that ATM. It is technically possible, just not currently supported.

Since your Capital One 360 DEBIT card has no fees, you can take out smaller amounts of cash as you need it instead of taking out a huge amount to cover your total estimated expenses in a single transaction so you do not end up with a lot of unspent money. London is a modern city and most places will take credit or debit for payments (you can use your US Starbucks card to get coffee in Great Britain and they give an excellent exchange rate! even Apple Pay works but with limitations) but it is always a good idea to have some amount of cash for the quick purchase of a snack etc.

Sweden is almost a cashless society. Most places there actually prefer you to use plastic, in my experience. The remainder of your stops are good with plastic but I have had better luck with cash in restaurants there.

It would be best not to exchange actual cash. The rates suck. What I have been doing is saving my cash for my next trip or selling it to friends who are traveling and want to arrive with some cash (using the Google rate at the time of the transaction).

So just go easy on the ATM withdrawals to reduce the leftover cash. And don't forget to inform Capital One about your travel plans so they don't cut you off.

I think the idea of getting the local currency you think you will need as soon as possible is a good one, and putting the leftover currency toward your hotel bill is excellent. You can even get rid of the coins this way. Remember that taxis may be cash-only, so be sure you have enough to cover last-minute expenses (like using the loo at a train station, usually 1Euro or the equivalent, (almost every train station in Europe).

Plenty of good advice, but 2 things to add: (1) If you have a PIN number other than 4 digits, there's no need to change it. I've never had a problem using my 6 digit code. (2) I believe that Capital One no longer wants you to tell them when you'll be out of the country, at least for credit cards (I'll make sure of this before my upcoming trip). I don't have a debit card with them, but I assume it would be the same.

The concept of a partner bank seems to be going away. Capital One (regular or 360) never had one. Even the Bank of America one doesn't completely cover the fees any more. But I have never been charged a fee by an ATM operator in Europe yet because I am careful about which ones I use and stick to those physically attached to a bank. I know in some countries, like Portugal and Spain, that is changing and many are reporting they do get charged a fee by the ATM. And it is true that Capital One 360 does not refund ATM fees for non Allpoint network transactions (Allpoint is a domestic US ATM network).

It is important to note that Capital One has several different account type. It is only the 360 account that guarantees no fees from them on foreign ATM transactions. Most other Capital One accounts do charge foreign fees on Debit cards. All Capital One Credit cards have zero foreign transaction fees.

yes, remaining coins can be converted to snacks at the airport, and there are usually some choice of charity drop boxes at airport (world wildlife fed or a children related charity)

On the subject of the debit cards... wjat is everybody's opinion on the Charles Schwab higj yield checking acct? No ATM fees.

Love it!! I have used my Schwab debit card for about 5 years of trips -- just store it in my money belt with my passport between trips.