Conditional INSERT INTO statement in postgres

As of 9.5 version of pgsql upsert is included, using INSERT ... ON CONFLICT DO UPDATE ...

The answer below is no longer relevant. Postgres 9.5 was released a couple years later with a better solution.

Postgres doesn't have "upsert" functionality without adding new functions.
What you'll have to do is run the select query and see if you have matching rows. If you do, then insert it.

I know you're not wanting an upsert exactly, but it's pretty much the same.

That specific command can be done like this:

insert into LeadCustomer (Firstname, Surname, BillingAddress, email)
select 
    'John', 'Smith', 
    '6 Brewery close, Buxton, Norfolk', '[email protected]'
where not exists (
    select 1 from leadcustomer where firstname = 'John' and surname = 'Smith'
);

It will insert the result of the select statement, and the select will only return a row if that customer does not exist.