Yes it is possible but you'll need to get the employers PAYE number. However it will need to be presented to your employer.
The easiest thing to do in this situation is to get your employers PAYE number, then call the PAYE section of your tax district and ask them issue a tax credit certificate to your new employer. This way you're employer won't know your previous salary. Make sure to get the cert issued on a week 1/ month 1 basis, otherwise you may end up owing the Revenue additional tax as a result of over claiming credits.
Then around March next week year (after P35 deadline) contact your tax office and ask them to issue you a P21 balancing statement. This will correct any problem that may have arisen due to the week 1/ month 1 tax treatment.
I say March because at this stage Revenue should have details of both of you incomes for 2008.
Regards,
Mini