Depends on school, most popular private use online pretest then follow by paper exams.
Online pretest can be ISEB or CEM select.
Paper exams normally the most selective private school will write its own open format papers, former example paper can be download from the school website.
Some fairly selective school use multiple choice papers, for example WHS use GL.
In most cases the exam format will be outlined in the School website in details, you just need to navigate through your target schools. For example, Highgate in their website has very details on exam format last year: NVR provided by GL, then follow by its own maths and English papers with exam for download.
Note that even school use the same example providers, e.g GL or CEM, the exam difficulty can be very different by schools, as the school can prescribe the level they want from the exam providers - via difficulty of the questions or the time intensity of the exam.
DD took GL NVR from Highgate last year, her comment was the questions is easier than the other Grammar school GL NVR exam. Though Highgate tests more questions, she got 40% more time per question to finish the paper compared to the grammar school exam she did, so no time pressure at all.