First of all you do not need " coinage" for tipping in dollars.
A minmum tip would be one WHOLE American dollar. No one would tip less as that would be an insult, even if all room service brought you was tea, tip would be 1$ min. you should tip 2 or 3 dollars min if they bring a full meal.
I am sure British Banks have American dollars.They seemed to last time I was in England 4 yrs ago, perhaps they do not now, but I doubt that, are you perhaps from a small town? A larger city may have what you need, remember thousands of American tourist dump their dollars in your country, so they gotta be floating around somewhere!
Since you do not need many perhaps try an exchange booth at the airport( I know the rate is not good but you don't need that many to start with, just get 10 or 20 pounds changed for handing out in dollars.
I am not familar with Euros, but I imagine since alot of your tours/ports are going to be to countries where the currency is Euros, then you should tip in Euros. Just get a bit to start off with, and really how many tips do you really need?
We are Canadian and don't quite get the tip tip tip thing, I mean we do tip room service, and we leave the shipboard tips on our account, but we rarely tip anyone else. Perhaps a tour leader, only if he was very good though, those shore exes are so exspensive that I do not feel the need to pay extra unless it was an especially good tour. and of course we tip a taxi driver, but it is usaully just added to the fair( rounded up) .
I realize that your coins come in bigger denominations , but the biggest in American ( that is widely available and used) is a 50 cent piece. Most common coinage is 25 , 10 and 5 cent coins. Not great tipping money. I recommend you not get any coins at all.
Anyways have fun and don't let the whole tipping thing drive you nuts.
Last year when we traveled to Europe we had to pay a tidy premium to our local bank to get a supply of Euros (we were arriving in Rome fairly late at night and our apartment had to be paid in cash). In speaking with a different banker this year he said he'd just charge the prevailing rate. And we live in a relatively small town. I won't pretend to know how this would be handled in the UK but even if you got large US bills, wouldn't the purser's office change that straight across? I understand that when they exchange currencies, it's different. But if you gave them a $50 and asked for 10s, 5s and 1s, I wouldn't think that would cost you anything extra. But I've no experience with that. And, honestly, now that alot of Europe is on Euros and pounds, it's not SUCH an inconvenience if the tippee(!) got them. Not like before when there were SO many different currencies. They go ashore also and need some amount of local currency. Good luck.
I keep reading posts where some old people think that it is "cool" to tip with strange currecny, such as a $2 bill, or a gold coin with $1, or a canadian $2 coin (tooner)>
I can assure you that the people with whom I have spoken on cruise ships find those type of tips to be a pain in the butt. They get excited at first because they think it is a $20 bill, and then get depressed to see it is just $2.
As for the fancy coins, these are a royal pain, because nobody wants them. You can't insert them into even a coke machine.