Mark Reckless accused Elin Jones of 'tilting the playing field' - and said it is "wrong" that she is a member of a political party.
The two have clashed over the time given to his AMs to question ministers.
The assembly said Ms Jones, a Plaid AM, acts with impartiality at all times in line with the rules of the institution.
Nigel Farage announced the formation of the group of four AMs during the European Parliament election campaign last month.
AMs in Plaid Cymru, and some in Labour, complained that the group had no democratic mandate having not fought an election under a Brexit Party banner.
The presiding officer - or Llywydd - gave permission for it to go ahead, and an attempt to stop the group from forming went nowhere.
The assembly's presiding officer is equivalent to the speaker of the House of Commons - overseeing the conduct of debates and the business of the Senedd chamber.This has been the practice since the inception
But unlike the Commons, presiding officers in the assembly have remained members of their political parties.
List of office holders
|Name||Picture||Entered office||Left office||Political party||Notes|
|The Rt Hon the Lord Elis-Thomas PCAM||12 May 1999||11 May 2011||Plaid Cymru||Elected unopposed 1999, re-elected unopposed 2003 and 2007|
|Dame Rosemary Butler DBE AM||11 May 2011||11 May 2016||Labour||Elected unopposed 2011. |
|Elin Jones AM||11 May 2016||Incumbent||Plaid Cymru||Elected 2016.|
Beat Dafydd Elis-Thomas 34 votes to 25 with 1 abstention 
Rosemary Butler retired from the Assembly in 2016
The BBC report that
Opposition party groups are able to nominate AMs to be spokespeople, who have rights to ask ministers questions during assembly proceedings.Last Wednesday, in a tense exchange in the Senedd, Mr Reckless attacked presiding officer Elin Jones for cutting the number of questions party spokespeople could ask.Mr Reckless said his group was able to ask ministers a "quarter" of what other parties could.It seems that Mr Reckless wants to use the term Presiding Officer rather than the Welsh Llywydd which most AMs use and the BBC should also follow suit
Presiding Officer, won't people conclude that you are biased as part of the Remain establishment," Mr Reckless told Ms Jones.The presiding officer replied saying the Brexit Party had been given the same allocation as UKIP - a party group until May - had recently.But she added: "I need to point out to you that I can only call your members if they make requests to ask questions, and, for the record, for members, I received no such requests from the Brexit Party today."
"You told us we couldn't," he responded.He told the BBC's Sunday Politics Wales programme that his group was "not being treated fairly".He said the Welsh Liberal Democrats were treated "completely the same" as others when it was a group of five."UKIP were only cut down in their spokespeople questions when they went down to a group of three. We're larger than that.""I think that it's wrong that the presiding officer is a member of Plaid Cymru - stays part of the Plaid Cymru group, has been able to employ people who are Plaid Cymru to come in and advise her," he said."A lot of things in the assembly are better than in Westminster, but one thing I thought was better in Westminster is the idea that the speaker is neutral and leaves their party.""I don't think it's right that she's tilted the playing field against the Brexit group," he added.A Welsh assembly spokesperson said: "The allocation of leaders and spokespeople's questions is at the discretion of the Llywydd who acts with impartiality at all times, in line with standing orders."The Llywydd can only call members to ask questions in the Siambr (chamber) if a request is received."In my mind the Brexit (Limited Company ) Party should never have been recognised as such but treated as Independents and are lucky the Llywydd has even recognised them.
They are are Waka-Jumpers who have no right to Party status.