It is no consequence that the BBC is often lauded as the best news source on the globe. It is the BBC's organizational structure which derives so much respect for the station all over the world, portraying the BBC as a publicly funded network, independent of the government.
The BBC is funded by the tax payer through TV licensing and Foreign Office funds. According to Wikipedia, "The licence fee represents approximately 75% of the BBC's income with most of the rest coming from the sale of its programming overseas and other business allied to broadcasting such as publishing."
The BBC has to justify receiving public funding, and showing (or pretending to show) neutrality its a primary way of doing so. Failing to do so jeopardizes their justification for charging the British public a TV licensing fee. If BBC bias is brought to widespread public attention, they would face extreme difficulty in procuring continued funds from the public. This is why the BBC spent £200,000 of Tax Payers money to quash independent reports of anti-Israel bias.
This is elaborated by BBC Watch's home page statement:
...the BBC consistently fails to adhere to its legal obligations to produce impartial and accurate reporting. Our systematic, objective and rigorous research points to the firm conclusion that the BBC frequently displays marked and consistent pro-Palestinian bias...
If the BBC were to provide a pro-Hamas charity with free advertising space, it would run the risk of being too anti-Israel to justify its public funding. Furthermore, as a result of not allowing this advertisement, the BBC is enjoying being publicly lambasted by pro-Hamas activists all over the country. Such complaints act as a counterweight against reports showing its consistent anti-Israel bias, and are therefore awarding the BBC with an illusion of neutrality and help justify its continued use of public funds.