The resignation came just a day after the parliament's new pounds 250m building in Strasbourg was opened by the French president, Jacques Chirac, and will fuel the debate about the workings of the 626-strong assembly.
Tuesday's opening ceremony was disrupted when more than 100 MEPs walked out in protest both at the the continuing French ban on British beef and at the fact that, roughly one week in four, the parliament decamps from its regular home in Brussels to Strasbourg.
Yesterday Mr Donnelly, one of the best-known British MEPs, went further, saying that he will quit as an MEP in January because the parliament cannot work properly in its split incarnation. His decision, which amazed colleagues, is likely to lead to a lively debate over the future of the institution and spark a bitter left-right battle over the succession.
Leading modernisers include Michael Cashman, the former EastEnders star who is also on Labour's National executive committee and Glenys Kinnock, although she is unlikely to stand.
The leftwinger challenger is expected to be Brian Simpson, who stood unsuccessfully when Mr Donnelly took over two years ago.
Mr Donnelly, an MEP of 10 years' standing, said: "I have campaigned for an am very proud of the powers that the new parliament has but, personally, I think that it is not going to work, because we cannot exercise these new powers split between two sites. Resigning will, perhaps, make some people sit up and think that here is a senior MEP who thinks that they have to look for activity elsewhere".
Mr Donnelly defended the institution itself, arguing: "MEPs have more powers than many MPs. We are based in Brussels, the home of the Commission, yet we have to go through this routine of sending ourselves off, exiling ourselves for a week every month to somewhere where the conditions - in terms of output - is less, because of this agreement.
"As we enlarge the EU I think this is going to be increasingly impossible to keep the two sites.
"I am very particular about the quality of what I do. In Strasbourg your capacity, your professional standards, is lower. You accept lower quality of output because, for example, you do not have all your files or all your staff. I am not prepared to do this any more. I am not prepared to compromise ... every three weeks and to accept that we have to make this ridiculous journey."
France has resisted any move to take dilute Strasbourg's status. The deal which enshrined it in EU law was agreed by John Major at the Edinburgh council of 1992.
Mr Donnelly, who discussed his decision with Tony Blair on Tuesday night, said he has no job to go to but is "obviously going to look at a number of options, including the commercial sector and politics".
Only on Tuesday the president of the parliament, Nicole Fontaine, defended its Strasbourg existence, saying Ernest Bevin, foreign secretary under Clement Attlee, had suggested the city as a site. Mr Donnelly said that was inaccurate, because "he was talking not about a European parliament but about an assembly of national parliamentarians which met infrequently, with no powers".
The catalyst for Mr Donnelly was a decision six months ago by the parliament not to vary its schedule for next year.
Last night he appealed for a change of the treaty in discussions next year. "As a parliament which has come of age, we still cannot decide where and when we should meet."Reuse content