If you have some other form of ID (a national insurance card and driving licence, e.g.) you could use these to satisfy your employer of your identity.
You should also show them a photocopy of your bio data page from your passport, your old residence permit, and the original letter from the Border Agency acknowledging your application, and the biometrics letter if you have it.
The Border Agency operates an "Employer checking service" that the employer can use to establish your right to work in the UK based on a pending application.
The form is here:
http://www.ukba.homeoffice.gov.uk/sitec ... equestform
More details on the ECS is here:
http://www.ukba.homeoffice.gov.uk/busin ... pport/ecs/