This is now complex as there's two parties.

Maybe the company would pay you more but the recruiter either:

- told them you're cheap, mistakenly or not

- wants to get you in cheap so they get follow on work

- doesn't know you expect a lot more

- is getting a bonus if they find suitable cheaper candidates

- doesn't yet know what you're telling us and so hasn't passed on the feedback on the poor offer.

- would be happy to fight for higher pay as they're paid a % of your annual rate.