The Curtain and the Theatre, both used by Shakespeare, have recently applied for redevelopment as modern drama spaces

The sites of two Jacobean theatres in London, both used by William Shakespeare, could host drama once again, following planning applications for new theatres.

The Curtain theatre in Shoreditch, once home turf for the Lord Chamberlain's Men, was discovered last year after an extensive archeological dig. Under plans submitted to Hackney council, it would be transformed into a 250-seat open-air amphitheatre, with an accompanying museum and exhibition space that would include the preserved and protected remains of the original theatre.

Meanwhile, just around the corner, it could soon be joined by a six-storey theatre with a 235-seat auditorium, on the site of a performance space known simply as the Theatre.

Launched a year before the Curtain, this was only the second permanent theatre built in England and hosted the Lord Chamberlain's Men when its proprietor Richard Burbage joined the company. The Theatre's remains were uncovered five years ago and various projects mooted, but fundraising and planning issues have delayed progress on the site. If these plans do go ahead, the building would include a glass floor that would ensure the original foundations remained visible to the public.

Both theatres were built outside of the city walls, in the so-called "liberties" outside control of the puritan City fathers.

Now firmly within the capital's bounds, both new spaces hope to present new work. The Theatre, which would keep its original name, would be a receiving house rather than originating its own work. Alan Taylor of the Belvedere Trust, the organisation behind the plans, said, "We expect to have a Shakespearian piece to what we are offering, but it will by no means be all Shakespeare."

Meanwhile, planners at The Curtain, to be called The Stage, have reportedly approached Shakespeare's Globe about jointly programming the space, but is aiming for similar plurality. Architect John Drew said: "It would be great if the performance space was used for all sorts of purposes, such as music as well as theatre."