Unfortunately the questions that are explicitly out for consultation don't include this section:
Exclusivity of Partnerships
3.3 The Government believes that individuals should only be able to enter into one partnership arrangement at any given time. Any individual who was still in a registered partnership or in a marriage should not be able to register a partnership with another person until that partnership or marriage had been legally dissolved. If an individual had been in a previous registered partnership or marriage, they would be required to provide evidence of the termination of
that partnership or marriage by death, nullity, divorce or dissolution.
3.4 The Government proposes to protect people from unwarily entering into relationships that are not exclusive. The couple would each be asked to declare that they were not:
(i) entering into a civil partnership before an existing partnership had been ended;
(ii) entering into a civil partnership while married.
3.5 In this way, registered partners will not find themselves subject to various sets of competing legal obligations and the importance of interdependent, stable relationships would be upheld.
... but that shouldn't stop you :)