British Embassy in Riyadh requesting bank statements for visitor visa

When applying for a UK visitor visa you are required to show evidence that you can support yourself for the entire duration of the trip. The purpose of the bank statements is also to verify your employment status: it would be suspicious if you claimed to be employed but don't receive a salary. To this purpose you usually submit recent bank statements (the UK governmental website gives 6 months of bank statements as an example).

There is no hard limit to how many bank statements to provide or how old they should be. The point being that you should provide all the documentation you deem necessary to uphold your application, no more no less. There is however a soft limit when it comes to old bank statements. Indeed the governmental UK Guide to supporting documents - visiting the UK states that bank statements older than one year should not be sent unless requested:

Section 4: documents you should not send unless specifically requested

This page provides guidance on the types of documents that are not required to consider your application.

[...]

• bank statements or letters issued more than 1 year before the date of application

The point here is that the ECO can request supporting information to your application, including old bank statements. Our advice here on TSE is to comply with the request of submitting extra documents. If the ECO is asking for more documents is to make an informed decision about your application. Chances are that refusing to submit these is likely to cause your visa to be refused.

I don't know if that's what you find puzzling but one thing that hasn't been made clear until now is that the financial means requirements for British visas are much broader than merely having cash in hand.

They want to know where the money comes from, whether you have a stable situation and whether the trip you are planning is commensurate with your means. Of course, they prefer applicants who are relatively well-off but being “too rich” compared to your legitimate sources of income is not good. So they like to see monthly transfers from your employer, whereas a large cash deposit would be a big red flag.

Bank statements can be used to assess all that.