Around 2.25% of the population was recorded as being resident in institutions of one sort or another on census night.
The 1921 Census of England & Wales distinguishes between Larger Establishments, Institutions and Prisons. All are characterized by having a population of inmates as opposed to family as occupants on census night. You can find a list of all institutions in the 1921 Census here
Some examples of returns categorized as institutions include asylums, barracks, boarding schools, colleges, hospitals, nursing homes, religious communities and workhouses.
Those considered larger establishments include hotels, hostels, registered lodging houses, Salvation Army shelters, and other places where there were expected to be 100 or more inmates upon census night and which were not regarded as formal institutions.
Different institutions recorded in the 1921 Census of England and Wales filled out their returns differently. Some may have been ordered alphabetically, some by date of admission, others such as hospitals may have been by ward.
In practice, the distinction between these two could be blurred. You may find institutional returns (with schedule type codes I, II and III, depending upon their size) or extended household returns (with schedule type codes EE, EEE, WW and WWW) used for a hotel, for example. There is a full list of 1921 Census schedule type codes here
As a result, searching for people in institutions can be difficult. Some families may not all be recorded on one return and the returns for some institutions run for dozens of pages and hundreds of individuals. In those cases, multiple forms were used that may appear as separate returns but are in fact a part of a larger institution.
Searching for the institutions themselves can be done in the same way as searching for any address.
The various returns that make up an institution required the same digitization and transcription process as separate household returns, therefore they are purchased and viewed individually.