I’m part of the central programme team. Broadly speaking the process is the same as it was when applying to access paper records (though CRIS removes the burden of deidentifying records, and makes them available in searchable, electronic formats).
There is no single repository of data and no single process for applying to access “all the data in CRIS”.
What this means is that each NHS Trust controls and manages access to the deidentified records that originated from them. For this reason you will need to contact the NHS Trust(s) which you want to work with directly, the NHS Trusts that have a CRIS instance can be seen here: https://crisnetwork.co/members, with links to their websites.
Each NHS Trust in the CRIS Network does have broadly the same process, but each NHS Trust may have their own local policies and procedures.
In some cases you may find the process easier if you are collaborating with someone at one of the associated research universities (though this is in no way mandatory).