To be eligible for a British Passport you MUST have British Nationality. If you are a highly skilled professional on a Tier 2 General visa you can apply for Permanent Residence in the UK after 5 years on Tier 2 General and then British Nationality after a further 1 year on Permanent Residence status.
After you have completed a certain number of years in the UK on a certain immigration status you can normally apply for Settlement (also known as ‘Indefinite Leave to Remain’ or ‘Permanent Residence’).
After you have spent a certain period of time in the UK (generally 5 years for skilled workers) you can normally apply for Indefinite Leave to Remain (also known as Permanent Residence). Following a further 1 year it is normally possible to apply for Naturalisation as a British Citizen and then a UK Passport.