If the girls get along well, and if your child interacts well with her grandfather and step-grandmother, I'd let her go.
BUT, I would do some preparation of my own beforehand.
1. Go to a large metropolitan bank or airport and get her a few coins and some paper currency that she'll see and use over there. Figure out a way to give her a rough estimate of equivalencies. For example, tell her "one of our dollars is equal to two of theirs (or whatever the ratio is). So if a candy bar costs one dollar here, how much would you pay me in the foreign currency?" (Don't worry about the little percents, just a basic whole number estimate. Go online to a UK site and show her the symbol for pounds and whatever else they use, and have her pretend that she's buying something from you. Set up a little pretend snack bar on your kitchen counter but only use signs labeled in British currency and only accept British currency for transactions, just for fun.
Role play: Come up with different scenarios. Like, the other girl wants to sneak out of the hotel, or try going to the pool without anyone knowing, or someone offers her something on the street, or she gets separated from her group and is lost. Actually pretend that it's happening. What should she do? What do the police look like? (google photos). Teach her some basics about safety, staying with her group, not getting distracted by strangers who may be pickpockets, etc. If she and the other girl go around in the hotel, what would be the boundaries (lobby, snack area, restaurant, etc., but not outside, for example).
Buy her one of those travel pouches that can be worn around the neck like a necklace or around her waist like a belt. (Airport gift shops are good places to find a wide variety of these things). Tell her to wear it 100% of the time, underneath clothes (not visible). It should contain her passport unless her grandfather puts it in a safe or assumes responsibility for it, a clearly labeled ID with contact information (both here and there) in permanent marker (I'd laminate it to make it waterproof), some money (not for spending on trinkets but for emergency cab fare or other emergency use).
Go to your cell phone provider and tell them where she'll be traveling and make 100% sure that her phone will work there, and make sure your plan is activated for that. Then teach her the proper way to make an international call, and program it in advance (and remember all the international codes and country codes and area codes) with your phone numbers and her grandparents' phones and the hotel phone. Practice using the phone. I know she probably is like a lot of kids and knows the phone inside and out, but dialing in and to a foreign country often involves extra numbers.
Provide her with a good quality but disposable camera (or 2 or 3). That way she doesn't have to worry about the camera being stolen, and if it got lost or dropped, it's only a few bucks from the store that you've lost. But she can still have a good time taking pictures.
If they know where they're going, have your daughter look up the region or city online and learn something about the cuisine, landmarks, climate, etc.
If she hasn't flown before, take her to the airport just to observe. Point out the security line and show her what to expect.
We've lived overseas, and my son has traveled to several countries with small groups. I think the role playing and practice beforehand for anything that might come up helped him have safe and happy trips every time. Just make sure that you don't come across as nervous. Tell her "just like we pack clothes for a trip, we also have to prepare in other ways. I want you to have a wonderful time, and that can happen if you are prepared, and familiar with the money and phones and some basic information." Act and speak confidently and she'll pick that up from you.