This will depend entirely on the kind of deal agreed and is not pregiven. These agreements are usually reciprocal. You need only look at the current rules UK applies - which differ from those of other EU and Schengen members, as it is not a signatory of the Schengen agreement. The UK effectively has its own tarrifs (where most other EU-Schengen members have the tarrifs described above) which are more expensive than those of other EU member states, as well as more strict. For example, the provisions for academics, students and NGO workers are not included in UK immigration laws.
The exception to this is for US Citizens who can travel to the UK with simply their passport - but they cannot work. In order to work they require a proper visa. Exemptions are also provided for any British Commonwealth, Territories and Dependencies (obviously - although India is excluded), and a number of states including Israel, Argentina, and Australia (although some, such as UAE, require EVW authorisation). Long story short, yes it is very possible but not 100% certain, and it will be likely reciprocal.