zivvy,
While I haven't had to go through the job search here in the UK (I was placed by my university at an internship), I can tell you that it is affecting my overall experience IN the workplace. Possibly it's just me being insecure, but I often feel my accent 'dumbs' me down, and people here don't take me seriously. Also, I am the only American, and only intern at my company, which doesn't help much. I sometimes sense an anti-American tone (Americans are greedy war-mongers, etc) but I think it's because no one here is used to working alongside Americans day by day. I would suggest researching, if possible, companies that often hire Americans, as they will be more open to getting to know you and assessing you by your skills not your accent!
Courtney