"However this proposal will fundamentally break the principle that for each government service, the data that is collected is only used for that service"
As long as the subsequent use to which data are put can be described as "not incompatible" with the original purpose for processing, you'd be surprised how much further data can be exploited (and I don't necessarily mean "exploited" pejoratively).
This presumes proper "fair processing" activity - transparency and openness about the subsequent use, a legal basis for it (be that consent, legislation, court order or whatever) but it's eminently doable, and always has been.
"Personal data shall be obtained only for one or more specified and lawful purposes, and shall not be further processed in any manner incompatible with that purpose or those purposes."
As usual, tons of knee-jerk in the comments here, but - trust me on this - the policy makers in the government organisations that become involved in these proposed novel datashares/uses are careful to an almost obsessively paranoid degree, about good governance and proper lawfulness/fairness considerations; and - trust me on this too - kick out unacceptable proposals on a daily basis.
And will continue to do so, even if this initiative rolls out.
Let me put it another way: Cabinet Office gets told "no" a lot...