This is a difficult proposition because, unlike most/all other European countries the UK has no obvious, clear, transparent and accessible system such as a national register where you go and get the whole process completed in a single operation. My son registered as a working adult in Denmark a few years back - he went to one office, waited about 45 minutes for his turn and then 15 minutes later he had finished, including registering with a doctor. Moreover, he now had everything (a single number) necessary to open a bank account, etc., etc. This stands in stark contrast with the UK where each institution, authority, etc. operates its own files and there is little or no connection between them. In practice, anyone living (or wanting to live) in the UK has to go traipsing to the different offices, usually having to repeat information/proof at each one and more. However, in all likelihood the first port of call for your daughter would be to speak to HMRC to see if she has already been issued with some form of tax/national insurance number and take it from there. I cannot imagine all of what she needs to establish is going to take less than several months, but I have no personal experience of this nor do I know anyone who does.