An aside but "Making Money" by Terry Pratchett references a similar sub-office of the Post Office in Ankh-Morpork--the Blind Letter Office. Amusingly, Lord Vetinari is able to assist with some as their addresses are mis-spelled vague directions rather than strict addresses.
A research briefing document from the House Of Common Library (https://researchbriefings.files.parliament.uk/documents/CBP-...) states that the Memorandum of Understanding on which the scheme relies states no upper limit on the amount of people that can be sent to Rwanda.