It depends on which biometric they wish to re-take
I will assume, for the remainder of this answer, that the person does not consent to having their biometrics taken. Otherwise, the law is less rigid.
In the context of fingerprints, refer to s61(3) of PACE 1984 (with my emphasis added in bold):
The fingerprints of a person detained at a police station may be taken without the appropriate consent if—
(a)he is detained in consequence of his arrest for a recordable offence; and
(b) he has not had his fingerprints taken in the course of the investigation of the offence by the police.
This means that, in general, the police may not take the person's fingerprints again if they have already taken them. However, the act lists two exceptions to the above in s61(3A):
Where a person mentioned in paragraph (a) of subsection (3) or (4) has already had his fingerprints taken in the course of the investigation of the offence by the police], that fact shall be disregarded for the purposes of that subsection if—
(a) the fingerprints taken on the previous occasion do not constitute a complete set of his fingerprints; or
(b)some or all of the fingerprints taken on the previous occasion are not of sufficient quality to allow satisfactory analysis, comparison or matching (whether in the case in question or generally).
Therefore, assuming that the person does not consent to have their fingerprints taken again, the above two scenarios are the two statutory exceptions that allow the police to collect their fingerprints again. It is worth noting that there are other exceptions to handle very particular sets of facts (eg ambiguity surrounding identical twins). However, the two above are the general exceptions. For the complete list of all exceptions, s61 is comprehensive.
This answer, of course, is focused on fingerprints as detailed in s61. The exact same principles apply to other forms of evidence. In s61A, the relevant law is outlined for footprints. Similarly, in s62, the relevant law is outlined in the context of intimate samples. As each is considered separately (and there are more than just these three), I cannot go into each biometric in this answer.
If you are looking for a specific type of evidence refer to the contents of PACE 1984 and refer to the relevant section.