My view is to be upfront about this… Remember an employer will read your CV and may well work out you are from overseas by simply looking at your previous education.
So if you are from outside the UK, be clear about your nationality on your CV whilst clarifying how this impacts your eligibility to work in the UK. For example, if applying for a part-time job whilst studying put something like:
Nationality: Indian, eligible to work part-time in the UK for up to X hours.
(Make sure you know the current position by always keeping up to date with information on the UK Borders website)
If you are looking for work in the UK after you have finished your studies, try something like
Nationality: Indian, Tier 1 (Post-Study Work) Migrant, eligible to work in the UK for 2 years.