A Regular Art in the Park sketcher and Barbican resident has kindly sent the following more detailed directions, for which many thanks. In her words:
"Below is a map showing the Beech Street Gardens indicating how to get there and 2 routes from the gardens into the Barbican Centre. The map is based on a photo of the user unfriendly map posted round the Barbican Centre, so I hope it is clear.
The best route in is via the steps from Barbican station leading up to the pedestrian bridge over Aldersgate Street. Anyone wanting to go to Moorgate Station on the Northern line is best advised to change at Moorgate on to a train to Barbican station as the route from Moorgate is tortuous..
I have shown a set of arrows leading along the level of the gardens, turning right under Frobisher Crescent, across the Sculpture Court which includes some unusual planting providing a vista for the redeveloped flats in Frobisher Court. Turning right before the conservatory (which unfortunately will be closed), there is an entrance to the 3rd floor of the Barbican Centre. Straight across from the entrance there are stairs and lifts to the ground floor of the Barbican Centre for the ground floor cafe and terrace. Alternatively, turning right towards the art gallery and then right again, there are toilets on the 3rd floor level. The gallery is currently showing an exhibition by Lee Krasner, but there is a charge.
The other set of arrows lead from the route from the pedestrian bridge to steps just before Defoe House. The steps split, the left hand side steps leading to the lower level Defoe Place, along the length of Defoe House to a set of steps leading down to the Barbican Centre Terrace and ground floor cafe. There are further toilets off the cafe."