The Hornets are due to face their Northern League rivals Consett for the title on May 3 as part of the annual Non-League Finals Day at the national stadium.
But current covid restrictions mean the match will have to be played behind closed doors – less than two weeks before up to 20,000 spectators could be preparing to watch the FA Cup final at the national stadium on May 15.
“I think the Government could have brought forward by a fortnight, [Hebburn Town’s] supporters being able to attend,” said South Tyneside councillor Wilf Flynn.
“It’s just an arbitrary date, I don’t see what it’s got to do with science, or science advice, and I see no reason why the Hebburn supporters couldn’t have been in Wembley on May 3, instead of two weeks later when it’s going to be allowed.”
Cllr Flynn was speaking at a meeting of South Tyneside Council’s Hebburn Community Area Forum (CAF), which was held by videolink and broadcast via YouTube.
Jarrow MP Kate Osborne, whose constituency includes Hebburn, has previously urged the Secretary of State for Culture, Media and Sport, Oliver Dowden, to work with the FA on getting more fans back to stadiums sooner.
Fans are expected to be allowed to attend the FA Cup semi finals later in April to trial the return of spectators, with reports suggesting up to 20,000 could be allowed to attend by the time of the FA Cup final on May 15.
The plight of clubs due to play on the finals day had been raised by his fellow Conservative MP Andrew Jones, who represents the Harrogate and Knaresborough constituency.
The Prime Minister replied: “I hope very much that the Football Association have listened carefully to what (Mr Jones) has to say and they do what they can.
“And I look forward to May 17 when spectators, according to the road map, may return.”