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Your local Job Centre can issue you with a NI Number, problem solved.
Otherwise here is a useful link:
Apply for a National Insurance number - GOV.UK (www.gov.uk)
Yes, well delays these days are commonplace. A NI number will be issued on the spot by a Job Centre.
Just the normal self assessment, the SA100 unless supplementary forms are needed viz:
Self Assessment forms and helpsheets - GOV.UK (www.gov.uk)