Who put the note on the bill saying the solicitor had granted permission? Was it your sister? If so, how do you know it is correct - could she have just made it up, or deliberately misinterpreted something the solicitor said?
I don't think you can criticise the solicitor unless you know for a fact that he did grant permission & your sister relied on it. If that is the case, then it seems to me the solicitor has exceeded his remit, particularly as you had written to him saying this was not to be done. You could write to the solicitor referring back to your earlier letter & saying that work has now been done which you understand was done because he granted permission. Ask him for his comments on this & ask him to confirm to you in writing that he will not authorise your sister to take any other action in relation to the estate.
However, if you can't get anything acceptable out of the solicitor doing anything else about it may be difficult. The best place to start may be to see if you can talk to a Law Society helpline (look on their website to see if there is anything). Otherwise, you may get involved in a lengthy & expensive dispute using your own solicitor. The other possible source of help is the Probate registry. They may be able to advise you on the responsibilities of executors where there are more than one & may comment on the solicitor's involvement.
As regards release of money from the bank, you need to find out from them what authority they would require, & put in writing to them (recorded delivery, keep a copy) that no money is to be released without the authority of you & your brother.