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

There is no obligation to transfer to the new owner under the Transfer of Undertakings (Protection of Employment) Regulations (TUPE). However, if you refuse to transfer your contract of employment comes to an end and you will be treated as having effectively resigned.

You would not normally be able to claim a redundancy payment. Whether you can bring a claim for unfair dismissal will depend on whether the consultation was fair and/or whether the new employer is proposing that you suffer a substantial negative change to your terms and conditions (eg relocation or a less generous pension).