Oxford University has promised there will be two routes through its Radcliffe Observatory Quarter after a Jericho councillor spoke of the importance of the site being open to the public.

Labour city councillor Susanna Pressel was speaking after the reopening of the newly refurbished Radcliffe Infirmary, which will be used for teaching humanities at Oxford University.

It was opened on Monday by university Vice-Chancellor Prof Andrew Hamilton and Prof Shearer West, head of the university’s Humanities Division.

It is one of the many new buildings that will be opened on the site by the university over the next few years, including the Mathematical Institute next year.

Ms Pressel said: “I think they have done a magnificent job of restoring the Radcliffe Infirmary building and the university is mindful of its very important history.

“It will be lovely to see the whole site back in use, but it will be many years before we see that. All the way through I have made the point of pressing for a shortcut for the public through the site and it will be restored in due course.”

Oxford University spokesman Matt Pickles said: “There will ultimately be two public walkways through the site.

“One is already open during daylight hours. It passes from Woodstock Road to Walton Street, emerging at New Radcliffe House.”

As part of the opening ceremony, the infirmary building’s well-known Triton fountain was turned on and a flag was raised on top of the building.

The former Radcliffe Infirmary has been completely refurbished as part of the university’s £220m renovation of the Radcliffe Observatory Quarter and it is now home to the Humanities Divisional Office, the Faculty of Philosophy and the Philosophy and Theology Libraries.

Work included replacing the 6ft Triton statue, which sat outside the building for 150 years, after restorers found it was beyond repair after freezing up in successive winters.

A new statue was commissioned at a cost of £45,000 and the original is being rehoused indoors at the Observatory Quarter.

Work is also being carried out on the Mathematical Institute building and the university has said the scheme is still on schedule.

Mike Wigg, the university’s head of capital projects, said: “The maths building will be completed next July for the following academic year.

“For the Blavatnik School of Government we have another public exhibition taking place at the start of next month, with a planning application going in towards the end of next month or early December. That will be ready for the academic year beginning in 2015.”