The simple answer to that is that HAL should fund any development 100%.
Heathrow and the rest of the BAA monopoly were sold off some years ago to various UK & foreign investors. As such we effectively declared to the rest of the world that these assets were surplus to requirements and therefore had no strategic value to the UK.
We may derive benefit from having them where they are, but they do not belong to the country. They are independent businesses and should thrive or fail as they are able to address the vagaries of the commercial environment they operate within. It's effectively like someone deciding to build a garage servicing cars. The local area will get benefit from its presence by being able to use its services, jobs will be created and other businesses and financial benefits may be drawn into the locality by virtue of its operation. BUT, does the taxpayer fund every local garage that starts up? NO. as a business you have to stand on your own two feet.
Simply put, Ferrovial of Spain, Qatar Holdings, The Quebec Investment Fund, The UK Universities' pension fund, & the investment companies of the Governments of Singapore and China should be footing the bill for the development of their asset.
If we pay for any development work, we should be getting the Title Deeds back for the airport.
We are far to quick to offer money for things that we used to own, but don't even get a fair whack of tax on operating profit for any more, and it needs to stop.
Otherwise we could end up in the farcical situation that Reichskancellor Frau Sturgeon has created with buying Prestwick.