Do we have to accept a position with the new employer in a transfer of business?

No there is no obligation to transfer over, under the Transfer of Undertakings (Protection of Employment) Regulations (TUPE), but if you refuse to transfer, your contract of employment comes to an end and you will be treated as having effectively resigned. There is no dismissal in law, so you cannot claim unfair dismissal, nor would you normally be able to claim a redundancy payment.