No!
First of all, she's a 19 year old adult. Let her figure it out. Second, when she lands in London, her existing M1 Maxx service will provide plenty of "startup" allotment. She can step off the plane, and her phone will work, including for voice calling to her +65 number. There will be no "bill shock"; M1 Maxx just shuts off for the remainder of the 30 day cycle if she runs out of data or minutes.
THEN, after she arrives, if she wants a U.K. phone number (with some data allotment), she'll have to get a SIM or eSIM there, after she arrives. (You've already explained your fears that the university won't be able to reach her, and that they might need a U.K. mobile number. I think those fears are unjustified, but that's what you wrote upthread.) She can ask the university's international student office for suggestions, and she can ask local students for their suggestions. A local SIM or eSIM will probably cost roughly ÂŁ10 for a 30 day "Pay As You Go" (PAYG) SIM with plenty of mobile data, in some cases unlimited data. Maybe less if she shops around a bit. But that's her problem to solve (see above).
In terms of technical preparation, all she needs to do is make sure her phone is a "dual SIM" phone, that it can at least accept another eSIM (or physical SIM). But even if not she'll be able to swap SIMs, and that's not horrible.
....Now stop worrying about this, please? PLEASE?!? You're freaking me out, and I'm just reading your posts. Let her be a responsible student who learns how to live life and enjoys her experience. She's not headed to the remote Amazon rainforest where she might need satellite communications.