Thing is that you don't need to integrate it all into a huge single IT system. That's where they have gone wrong. A single huge database is nonsensical and there's simply no need for it.
It's the data that needs to be shared, and that can far more easily be done by data links between systems. What you need is "common" tagging of the data and a common method of identifying the data, with a suitable "data highway" that transmit data as required between the different systems.
That's the direction of the NHS databases these days. Different "providers" or departments can access the data they need (and only that) from other connected systems. It's very slow progress.
Early stages were as simple as there being a database of pharmacies, linked to GP surgeries, so the GP surgery can select a patient's preferred pharmacy from the list, and then establish a data link so that future prescriptions can be "pinged" to the pharmacy rather than walking round or faxing a paper prescription. That's a very simplistic example of data sharing, and took a long time to set up, but it's been a revelation. Pharmacists don't have access to your GP records, but have access to specific data they need, i.e. the prescription!
That kind of data linking is happening across the NHS. It's a shame that so much time and effort was wasted on a super NHS network linked database, but years ago, it was thought to be the "right" way to proceed, but now we have better software, better internet, etc and means of data transfer is completely different compared with 20 years ago!