I think that it is probably right that they do need this - but only after they have decided to make a job offer. It sounds perfectly unreasonable until then. The reason why they need it is to avoid the same mistake Baroness Scotland made - the onus is on an employer is establish that the employee has the right not only to be in the UK but also to work in the UK.
Maybe point out that, in this age of identify theft, your Mum would be happy to comply once the job offer had been made and your Mum knows exactly who the organisation is.