Before you do anything else, it is critical you confirm with the recruiter whether or not they have already submitted you to the company in question. If the recruiter has already submitted your resume to the company, you should proceed with that recruiter (I was working with two recruiters at once during a job search, and one submitted my resume without permission. The second helped me improve my resume, and submitted me to the same company with permission - I did not receive the job because the company had two competing resumes, and had already turned me down to the first recruiter based on my unimproved resume.).
From the recruiter's question, it sounds more likely your resume has not already been submitted. If that is the case, you are free to choose either option.
Using the Recruiter
Using the recruiter may be to your advantage if the recruiter has a good relationship with the company or hiring manager. It would likely be within their interest to negotiate a good salary, as they usually get paid a finder's fee based on that salary if you work out. The company is paying the recruiter, however, so you are less likely to be able to negotiate things like moving expenses or signing bonuses.
Applying directly with the Company
Salary negotiation would be completely up to you. You won't have a recruiter to push your resume toward the top of the pile. If your resume stands up solidly on its own, this is not much of a problem. You will want to have a clear idea of what pay you are expecting - don't forget to take into account cost of living differences between where you are now and where you would move - to make sure you don't accept an offer that doesn't work for your needs.
As the company does not have the added expense of the recruiter's fee to pay upon hiring or retaining you for a certain period of time, there may be more room in their budget to allow for things like signing bonuses or moving expenses.
In general, it sounds like you are unimpressed with this recruiter. If you have a negative impression of them, I would avoid them. But if you don't believe you would be able to negotiate for the pay or bonuses you should receive to full effect, going with the recruiter may be to your advantage. If you have doubts of your own negotiating ability, you may also want to consider finding a recruiter that makes a better impression to submit your application to the company.
Note: I am in the US. I know labor laws and common practices are significantly different in the UK and/or Europe, so please take that into account.