Right to work documentation includes a UK or EEA passport or national identity document as all UK and EEA nationals have the right to work in the UK without a work visa. If you were a non EEA national, you would need to show your passport with a visa which stated your permission to work (or not) in the UK. Letters from any other institution do not count as right to work documentation. The possession of a National Insurance card does not confirm your right to work either as you may have been issued one but your right to work is no longer valid.