They should have been able to make the data correspond.
I find it absolutely inconceivable that there is not, somewhere in the vaults at QMUL, a single file with all of the variables in it. That's how you analyze data from any study of any kind, unless there's some absolutely huge number of participants or variables.
Another very quick thought. We may have to be prepared for the possibility that QMUL may not actually be able to guarantee a particular sort order! Someone who better understands databases will know this better, but I'm guessing that when data is queried out of a db there will be a default sort applied, which likely depends on the parameters chosen and their values. Different parameters / values might well lead to a different sort order, and the person doing the querying not knowing (or caring) how things got sorted.
The data shouldn't be stored in a "database", in the sense of a traditional computer database management system where you have multiple tables and need keys to tie the various tables together. It will have been analyzed from a single file in the proprietary format of whichever software they used. Unusually, they report using Stata, SAS, and SPSS, which probably means they used a CSV file (a very plain, neutral file format that any statistical software package can read, including Excel) to transfer the data between the different pieces of software.
If that's the case (and if it isn't, they have a very weird setup), then the process of sending out variables selectively ought to be easy. Start with the master file sorted by participant ID, make a copy, and in that copy, delete all the variables except the ones you want to share. If you reassemble multiple chunks that were made that way, you will get back the original records.
It is quite deliberate that they've made it so the data sets cannot be combined. I knew they had some sort of trick up their sleeves, I guess this is it.
The fact that the sort order in the new files is not the same as the first file is either down to incompetence or malice. I always prefer the first of these explanations, but the level of incompetence (probably by multiple people) required in order for the newly-released variables not to be sorted correctly makes me wonder here.
I guess there's also a danger that a repeated similar request could be viewed as 'vexatious'?
This reminds me of a situation in another part of my life, which is a game where I have to gently ask people not to bend the rules. It's complicated, but let's say the maximum X they are allowed is 100, and they send in 115, so I say "No, please make it less than 100". They change it to 108 and I say "Please try again". They change it to 103 and I say "Please get it below 100", and then they go onto a forum and it's "The moderator is being such a nitpicker".
If this kind of argument gets wheeled out, it will be important to make sure the judge (etc) understands that it's not nitpicking or vexatious to point out that if the request was only 98% complied with, and the 2% missing (i.e., the correct sort) means that the other 98% is useless, then the request as a whole was not complied with.