There is legislation governing the rights of employees in your situation called TUPE (Transfer of undertakings for permanent employees). However it only covers permanent employees, agency/fixed term contracts may not be covered by it
Your service and T&Cs for the most part go across with 2 noticable exceptions. in regards to your pension, normally you would cease being a member of your current companies pension scheme but could join your new employers scheme (you may be entitled to transfer your funds across). Secondly, any redundacy scheme your current employer offers normally doesn't transfer over.
There may also be small things that your new employer can't replicate and may need to be negotiated away. eg, when I got outsourced from a bank to a non bank many years ago, the bank used to offer staff loans at lower rates, the new employer didn't and that entitlement had to be negotiated/bought out.