The expertise element you mention is not relevant to admission for mere attendance of the conference. It is relevant to the “permitted paid engagements” section, which says:
VISITORS APPENDIX 4. PERMITTED PAID ENGAGEMENTS
1 The following are permitted paid engagements:
- (a) an academic who is highly qualified within his or her field of expertise may examine students and/or participate in or chair selection panels, if they have been invited by a UK Higher Education Institution or a UK based research or arts organisation as part of that institution or organisation’s quality assurance processes.
- (b) An expert may give lectures in their subject area, if they have been invited by a UK Higher Education Institution; or a UK based research or arts organisation provided this does not amount to filling a teaching position for the host organisation.
As such proving expertise is not relevant to the situation you outline.
This is of course assuming that provision of air fare and hotel is not seen as payment, but in general the UK happily separates between expenses and payment.
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