Recruiters dont ask for any documents other than, sometimes, visa to show you are legally entitled to work here. They are not interested in verifying your background.
Once the potential employer makes an offer and you accept, it is at that point your new employer will ask for the following docs. It is highly varied in the UK so it can any or all of the below, just depends on the company really
1. Original Educational Certificate for your College Degree like Engg, MSc etc
2. Visa copy to show you can legally work here
3. Relieving letter once your previous company gives it - this is because you could be serving probation while interviewing so they will be happy to wait. Many companies dont even bother
4. References from colleagues - to confirm you worked at the position you stated OR point 7 below
5. As part of their checks that you need not worry about they also check if you have a criminal record in the UK
6. They also check if you at any point were declared bankrupt or owe a lot of money or have any court cases etc - all standard stuff for the UK
7. This is important - to verify your previous work and designation, they may contact HR of previous company to state what you worked as, position and salary earned. This is not always true. Either they ask HR or only ask the people you have provided them. If they ask HR, then they may either ask HR of last company worked or, very rarely, all companies worked
Some employers in the UK do not bother about previous salary and so dont ask for payslips. Otherwise as well, they may ask you how much you earned but they never ask for payslips or bank statements here. Legally, the new employer has no right to ask you about your previous package or ask proof for the salary earned as this is confidential data. Not many know this but those who are smart are aware of this very important rule. You can even tell the HMRC to not give any salary data out and if they persist and dont offer a job because of this, then you can put a case for discrimination
All the best
KP