Does a Lasting Power of Attorney allow this?

elsien

If the attorney is acting incorrectly in taking actions while the donor still has capacity which the donor does not agree with, then the donor should seriously  consider whether this is someone they want to be their power-of-attorney at all.

If it was me I’d be revoking the LPA and choosing a different replacement  attorney. There is also of course also the option of going to the OPG and informing them that the attorney is acting incorrectly. 

He could could also contact NS&I and tell them this was done without his consent, and discuss the possibilities of having the other person’s name removed from the account.

AnnieBard

RAS said:

Who is the alternative attorney?

Another relative, who I believe will also in future be an executor and will beneficiary.

Malthusian

In fairness, attorneys are not expected to be financial experts, and I can understand an attorney mistakenly thinking that putting both their name and the donor's name on the application form was the right thing to do...*

AnnieBard said:

The same attorney also intends to use the donor’s money to open an ISA in his (the attorney’s) sole name.

...Never mind, screw that noise. That's theft.
This is why lasting powers of attorney should always be registered and take effect immediately (not just when you have lost capacity); it gives you the chance to flush out nonsense like this and replace the attorney while you are still able to.
As above the donor should immediately withdraw all the money into a sole name account (immediately as in today, before the attorney decides that any more money is better off "resting" in their own sole name account), then contact the OPG to remove the troublesome attorney. They can then open a new sole name account with NS&I if needed.
*To expand: the donor's money should of course always be held in their sole name and not jointly with their attorney(s) (which would constitute a partial gift to the attorney). However, some application forms for financial products (particularly those targeted at individuals d'un certain age) ask for details of any attorneys to be entered separately on the application form. So it is possible that an attorney might innocently think that by entering their details on an application form, they are just telling the provider "these are the people who have authority to deal with the account" not "these are the people who own the account". However, that excuse can't apply to an attorney moving the donor's money into their own ISA.

Keep_pedalling

The should also get a new will or codicil to remove this person from being an executor, because they are either dishonest or incompetent and not fit to to be an attorney or executor.